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1. Black-Litterman Model: Practical Asset Allocation Model Beyond Traditional Mean-Variance Abdumuminov, Shuhrat PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_0_j_idt606",{id:"formSmash:items:resultList:0:j_idt606",widgetVar:"widget_formSmash_items_resultList_0_j_idt606",onLabel:"Abdumuminov, Shuhrat ",offLabel:"Abdumuminov, Shuhrat ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_0_j_idt609",{id:"formSmash:items:resultList:0:j_idt609",widgetVar:"widget_formSmash_items_resultList_0_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Mälardalen University, School of Education, Culture and Communication.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:0:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Esteky, David EmanuelMälardalen University, School of Education, Culture and Communication.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:0:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Black-Litterman Model: Practical Asset Allocation Model Beyond Traditional Mean-Variance2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAbstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_0_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:0:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_0_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This paper consolidates and compares the applicability and practicality of Black-Litterman model versus traditional Markowitz Mean-Variance model. Although well-known model such as Mean-Variance is academically sound and popular, it is rarely used among asset managers due to its deficiencies. To put the discussion into context we shed light on the improvement made by Fisher Black and Robert Litterman by putting the performance and practicality of both Black- Litterman and Markowitz Mean-Variance models into test. We will illustrate detailed mathematical derivations of how the models are constructed and bring clarity and profound understanding of the intuition behind the models. We generate two different portfolios, composing data from 10-Swedish equities over the course of 10-year period and respectively select 30-days Swedish Treasury Bill as a risk-free rate. The resulting portfolios orientate our discussion towards the better comparison of the performance and applicability of these two models and we will theoretically and geometrically illustrate the differences. Finally, based on extracted results of the performance of both models we demonstrate the superiority and practicality of Black-Litterman model, which in our particular case outperform traditional Mean- Variance model.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:0:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_0_j_idt869_0_j_idt872",{id:"formSmash:items:resultList:0:j_idt869:0:j_idt872",widgetVar:"widget_formSmash_items_resultList_0_j_idt869_0_j_idt872",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:0:j_idt869:0:fullText"});}); 2. A Variant of Updating Page Rank in Evolving Tree graphs Abola, Benard PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_1_j_idt606",{id:"formSmash:items:resultList:1:j_idt606",widgetVar:"widget_formSmash_items_resultList_1_j_idt606",onLabel:"Abola, Benard ",offLabel:"Abola, Benard ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_1_j_idt609",{id:"formSmash:items:resultList:1:j_idt609",widgetVar:"widget_formSmash_items_resultList_1_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:1:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Biganda, PitosMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.Engström, ChristopherMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Anguzu, CollinsDepartment of Mathematics, Makerere University, Kampala, Uganda.Mango, John MageroDepartment of Mathematics, Makerere University, Kampala, Uganda.Kakuba, GudwinDepartment of Mathematics, Makerere University, Kampala, Uganda.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:1:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A Variant of Updating Page Rank in Evolving Tree graphs2019In: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019 / [ed] Christos H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2019, p. 31-49Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_1_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:1:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_1_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PageRank update refers to the process of computing new PageRank values after change(s) (addition or removal of links/vertices) has occurred in real life networks. The purpose of the updating is to avoid recalculating the values from scratch. To efficiently carry out the update, we consider PageRank as the expected number of visits to target vertex if multiple random walks are performed, starting at each vertex once and weighing each of these walks by a weight value. Hence, it might be looked at as updating non-normalised PageRank. In the proposed approach, a scaled adjacency matrix is sequentially updated after every change and the levels of the vertices being updated as well. This enables sets of internal and sink vertices dependent on their roots or parents, thus vector-vector product can be performed sequentially since there are no infinite steps from one vertex to the other.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:1:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 3. A Variant of Updating PageRank in Evolving Tree Graphs Abola, Benard PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt606",{id:"formSmash:items:resultList:2:j_idt606",widgetVar:"widget_formSmash_items_resultList_2_j_idt606",onLabel:"Abola, Benard ",offLabel:"Abola, Benard ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt609",{id:"formSmash:items:resultList:2:j_idt609",widgetVar:"widget_formSmash_items_resultList_2_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:2:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Biganda, PitosMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.Engström, ChristopherMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Mango, John MageroDepartment of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.Kakuba, GodwinDepartment of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:2:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A Variant of Updating PageRank in Evolving Tree Graphs2021In: Applied Modeling Techniques and Data Analysis 1: Computational Data Analysis Methods and Tools / [ed] Yannis Dimotikalis, Alex Karagrigoriou, Christina Parpoula, Christos H. Skiadas, John Wiley & Sons, Inc. Hoboken, NJ, USA , 2021, Vol. 7, p. 3-22Chapter in book (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:2:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_2_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); A PageRank update refers to the process of computing new PageRank valuesafter a change(s) (addition or removal of links/vertices) has occurred in real-lifenetworks. The purpose of updating is to avoid re-calculating the values from scratch.To efficiently carry out the update, we consider PageRank to be the expected numberof visits to a target vertex if multiple random walks are performed, starting at eachvertex once and weighing each of these walks by a weight value. Hence, it mightbe looked at as updating a non-normalized PageRank. We focus on networks of treegraphs and propose an approach to sequentially update a scaled adjacency matrix afterevery change, as well as the levels of the vertices. In this way, we can update thePageRank of affected vertices by their corresponding levels.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:2:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 4. PageRank in evolving tree graphs Abola, Benard PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt606",{id:"formSmash:items:resultList:3:j_idt606",widgetVar:"widget_formSmash_items_resultList_3_j_idt606",onLabel:"Abola, Benard ",offLabel:"Abola, Benard ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt609",{id:"formSmash:items:resultList:3:j_idt609",widgetVar:"widget_formSmash_items_resultList_3_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:3:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Biganda, PitosMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.Engström, ChristopherMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Mango, John MageroDepartment of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.Kakuba, GodwinDepartment of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:3:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PageRank in evolving tree graphs2018In: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Springer, 2018, Vol. 271, p. 375-390Chapter in book (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:3:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_3_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this article, we study how PageRank can be updated in an evolving tree graph. We are interested in finding how ranks of the graph can be updated simultaneously and effectively using previous ranks without resorting to iterative methods such as the Jacobi or Power method. We demonstrate and discuss how PageRank can be updated when a leaf is added to a tree, at least one leaf is added to a vertex with at least one outgoing edge, an edge added to vertices at the same level and forward edge is added in a tree graph. The results of this paper provide new insights and applications of standard partitioning of vertices of the graph into levels using breadth-first search algorithm. Then, one determines PageRanks as the expected numbers of random walk starting from any vertex in the graph. We noted that time complexity of the proposed method is linear, which is quite good. Also, it is important to point out that the types of vertex play essential role in updating of PageRank.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:3:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 5. Updating of PageRank in Evolving Tree graphs Abola, Benard PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt606",{id:"formSmash:items:resultList:4:j_idt606",widgetVar:"widget_formSmash_items_resultList_4_j_idt606",onLabel:"Abola, Benard ",offLabel:"Abola, Benard ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt609",{id:"formSmash:items:resultList:4:j_idt609",widgetVar:"widget_formSmash_items_resultList_4_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Makerere University, Kampala, Uganda.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:4:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Biganda, PitosMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.Engström, ChristopherMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Mango, John MageroMakerere University, Kampala, Uganda.Kakuba, GodwinMakerere University, Kampala, Uganda.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:4:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Updating of PageRank in Evolving Tree graphs2020In: Data Analysis and Applications 3: Computational, Classification, Financial, Statistical and Stochastic Methods / [ed] A. Makrides, A. Karagrigoriou, C.H. Skiadas, John Wiley & Sons, 2020, p. 35-51Chapter in book (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:4:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_4_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Summary Updating PageRank refers to a process of computing new PageRank values after changes have occurred in a graph. The main goal of the updating is to avoid recalculating the values from scratch. This chapter focuses on updating PageRank of an evolving tree graph when a vertex and an edge are added sequentially. It describes how to maintain level structures when a cycle is created and investigates the practical and theoretical efficiency to update PageRanks for an evolving graph with many cycles. The chapter discusses the convergence of the power method applied to stochastic complement of Google matrix when a feedback vertex set is used. It also demonstrates that the partition by feedback vertex set improves asymptotic convergence of power method in updating PageRank in a network with cyclic components.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:4:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 6. Nonlinearly Perturbed Markov Chains and Information Networks Abola, Benard PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt606",{id:"formSmash:items:resultList:5:j_idt606",widgetVar:"widget_formSmash_items_resultList_5_j_idt606",onLabel:"Abola, Benard ",offLabel:"Abola, Benard ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt609",{id:"formSmash:items:resultList:5:j_idt609",widgetVar:"widget_formSmash_items_resultList_5_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:5:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Biganda, PitosMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.Silvestrov, DmitriiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Mango, JohnDepartment of Mathematics, Makerere University, Kampala, Uganda.Kakuba, GudwinDepartment of Mathematics, Makerere University, Kampala, Uganda.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:5:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Nonlinearly Perturbed Markov Chains and Information Networks2019In: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019 / [ed] Christos H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2019, p. 51-79Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:5:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_5_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding a special damping matrix multiplied by a small damping (perturbation) parameter ε. In this paper, we present results of the detailed perturbation analysis of Markov chains with damping component and numerical experiments supporting and illustrating the results of this perturbation analysis.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:5:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 7. Chapter 2. Nonlinearly Perturbed Markov Chains and Information Networks Abola, Benard PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_6_j_idt606",{id:"formSmash:items:resultList:6:j_idt606",widgetVar:"widget_formSmash_items_resultList_6_j_idt606",onLabel:"Abola, Benard ",offLabel:"Abola, Benard ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_6_j_idt609",{id:"formSmash:items:resultList:6:j_idt609",widgetVar:"widget_formSmash_items_resultList_6_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:6:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Biganda, PitosMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Silvestrov, DmitriiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.Engström, ChristopherMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Mango, John MageroDepartment of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.Kakuba, GodwinDepartment of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:6:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Chapter 2. Nonlinearly Perturbed Markov Chains and Information Networks2021In: Applied Modeling Techniques and Data Analysis 1: Computational Data Analysis Methods and Tools / [ed] Yannis Dimotikalis, Alex Karagrigoriou, Christina Parpoula, Christos H. Skiadas, Hoboken, NJ: John Wiley & Sons, 2021, p. 23-55Chapter in book (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_6_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:6:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_6_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This chapter is devoted to studies of perturbed Markov chains, commonly used for the description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularized by adding aspecial damping matrix, multiplied by a small damping (perturbation) parameter ε. In this chapter, we present the results of detailed perturbation analysis of Markov chains with damping component and numerical experiments supporting and illustrating the results of this perturbation analysis.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:6:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 8. Asymptotics of implied volatility in the Gatheral double stochastic volatility model Albuhayri, Mohammed PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt606",{id:"formSmash:items:resultList:7:j_idt606",widgetVar:"widget_formSmash_items_resultList_7_j_idt606",onLabel:"Albuhayri, Mohammed ",offLabel:"Albuhayri, Mohammed ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Mälardalen University, School of Education, Culture and Communication.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:7:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:7:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Asymptotics of implied volatility in the Gatheral double stochastic volatility model2022Doctoral thesis, comprehensive summary (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:7:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_7_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We consider a market model of financial engineering with three factors represented by three correlated Brownian motions. The volatility of the risky asset in this model is the sum of two stochastic volatilities. The dynamic of each volatility is governed by a mean-reverting process. The first stochastic volatility of mean-reversion process reverts to the second volatility at a fast rate, while the second volatility moves slowly to a constant level over time with the state of the economy.

The double mean-reverting model by Gatheral (2008) is motivated by empirical dynamics of the variance of the stock price. This model can be consistently calibrated to both the SPX options and the VIX options. However due to the lack of an explicit formula for both the European option price and the implied volatility, the calibration is usually done using time consuming methods like Monte Carlo simulation or the finite difference method.

To solve the above issue, we use the method of asymptotic expansion developed by Pagliarani and Pascucci (2017). In paper

**A**, we study the behaviour of the implied volatility with respect to the logarithmic strike price and maturity near expiry and at-the-money. We calculate explicitly the asymptotic expansions of implied volatility within a parabolic region up the second order. In paper**B**we improve the results obtain in paper A by calculating the asymptotic expansion of implied volatility under the Gatheral model up to order three. In paper**C**, we perform numerical studies on the asymptotic expansion up to the second order. The Monte-Carlo simulation is used as the benchmark value to check the accuracy of the expansions. We also proposed a partial calibration procedure using the expansions. The calibration procedure is implemented on real market data of daily implied volatility surfaces for an underlying market index and an underlying equity stock for periods both before and during the COVID-19 crisis. Finally, in paper**D**we check the performance of the third order expansion and compare it with the previous results.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:7:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_7_j_idt869_0_j_idt872",{id:"formSmash:items:resultList:7:j_idt869:0:j_idt872",widgetVar:"widget_formSmash_items_resultList_7_j_idt869_0_j_idt872",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:7:j_idt869:0:fullText"});}); 9. An Improved Asymptotics of Implied Volatility in the Gatheral Model Albuhayri, Mohammed PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt606",{id:"formSmash:items:resultList:8:j_idt606",widgetVar:"widget_formSmash_items_resultList_8_j_idt606",onLabel:"Albuhayri, Mohammed ",offLabel:"Albuhayri, Mohammed ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt609",{id:"formSmash:items:resultList:8:j_idt609",widgetVar:"widget_formSmash_items_resultList_8_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:8:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Engström, ChristopherMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Malyarenko, AnatoliyMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Ni, YingMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:8:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); An Improved Asymptotics of Implied Volatility in the Gatheral Model2022In:*Springer Proceedings in Mathematics and Statistics*, Springer Nature, 2022, Vol. 408, p. 3-13Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:8:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_8_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We study the double-mean-reverting model by Gatheral. Our previous results concerning the asymptotic expansion of the implied volatility of a European call option, are improved up to order 3, that is, the error of the approximation is ultimately smaller that the 1.5th power of time to maturity plus the cube of the absolute value of the difference between the logarithmic security price and the logarithmic strike price.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:8:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 10. Asymptotics of Implied Volatility in the Gatheral Double Stochastic Volatility Model Albuhayri, Mohammed PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt606",{id:"formSmash:items:resultList:9:j_idt606",widgetVar:"widget_formSmash_items_resultList_9_j_idt606",onLabel:"Albuhayri, Mohammed ",offLabel:"Albuhayri, Mohammed ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt609",{id:"formSmash:items:resultList:9:j_idt609",widgetVar:"widget_formSmash_items_resultList_9_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:9:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Malyarenko, AnatoliyMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Ni, YingMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Engström, ChristopherMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Tewolde, FinnanMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Zhang, JiahuiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:9:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Asymptotics of Implied Volatility in the Gatheral Double Stochastic Volatility Model2019In: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019 / [ed] Christos H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2019, p. 81-90Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:9:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_9_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The double-mean-reverting model by Gatheral [1] is motivated by empirical dynamics of the variance of the stock price. No closed-form solution for European option exists in the above model. We study the behaviour of the implied volatility with respect to the logarithmic strike price and maturity near expiry and at-the- money. Using the method by Pagliarani and Pascucci [6], we calculate explicitly the first few terms of the asymptotic expansion of the implied volatility within a parabolic region.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:9:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 11. Asymptotics of Implied Volatility in the Gatheral Double Stochastic Volatility Model Albuhayri, Mohammed PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt606",{id:"formSmash:items:resultList:10:j_idt606",widgetVar:"widget_formSmash_items_resultList_10_j_idt606",onLabel:"Albuhayri, Mohammed ",offLabel:"Albuhayri, Mohammed ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt609",{id:"formSmash:items:resultList:10:j_idt609",widgetVar:"widget_formSmash_items_resultList_10_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:10:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Malyarenko, AnatoliyMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Ni, YingMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Engström, ChristopherMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Tewolde, FinnanMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Zhang, JiahuiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:10:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Asymptotics of Implied Volatility in the Gatheral Double Stochastic Volatility Model2021In: Applied Modeling Techniques and Data Analysis 2: Financial, Demographic, Stochastic and Statistical Models and Methods / [ed] Dimotikalis, Yannis, Karagrigoriou, Alex, Parpoula, Christina, Skiadas, Christos H., Hoboken, NJ, USA: John Wiley & Sons, 2021, p. 27-38Chapter in book (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:10:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_10_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The double-mean-reverting model by Gatheral is motivated by empirical dynamics of the variance of the stock price. No closed-form solution for European option exists in the above model. We study the behaviour of the implied volatility with respect to the logarithmic strike price and maturity near expiry and at-the-money. Using the method by Pagliarani and Pascucci, we calculate explicitly the first few terms of the asymptotic expansion of the implied volatility within a parabolic region.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:10:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 12. Numerical Studies of the Implied Volatility Expansions up to Third Order under the Gatheral Model Albuhayri, Mohammed PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt606",{id:"formSmash:items:resultList:11:j_idt606",widgetVar:"widget_formSmash_items_resultList_11_j_idt606",onLabel:"Albuhayri, Mohammed ",offLabel:"Albuhayri, Mohammed ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt609",{id:"formSmash:items:resultList:11:j_idt609",widgetVar:"widget_formSmash_items_resultList_11_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:11:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Dimitrov, MarkoMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Ni, YingMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Malyarenko, AnatoliyMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:11:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Numerical Studies of the Implied Volatility Expansions up to Third Order under the Gatheral Model2022Conference paper (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:11:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_11_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The Gatheral double stochastic volatility model is a three-factor model with mean-reverting stochastic volatility that reverts to a stochastic long-run mean. Our previous paper investigated the performance of the first and second-order implied volatilities expansions under this model. Moreover, a simple partial calibration method has been proposed. This paper reviews and extends previous results to the third-order implied volatility expansions under the same model. Using Monte-Carlo simulation as the benchmark method, extensive numerical studies are conducted to investigate the accuracy and properties of the third-order expansion.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:11:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 13. The mathematics of internet search engines Andersson, Fredrik K. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_12_j_idt606",{id:"formSmash:items:resultList:12:j_idt606",widgetVar:"widget_formSmash_items_resultList_12_j_idt606",onLabel:"Andersson, Fredrik K. ",offLabel:"Andersson, Fredrik K. ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_12_j_idt609",{id:"formSmash:items:resultList:12:j_idt609",widgetVar:"widget_formSmash_items_resultList_12_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); WorldLight.com AB, Sweden.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:12:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:12:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); The mathematics of internet search engines2008In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, ISSN 0167-8019, E-ISSN 1572-9036, Vol. 104, no 2, p. 211-242Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_12_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:12:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_12_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This article presents a survey of techniques for ranking results in search engines, with emphasis on link-based ranking methods and the PageRank algorithm. The problem of selecting, in relation to a user search query, the most relevant documents from an unstructured source such as the WWW is discussed in detail. The need for extending classical information retrieval techniques such as boolean searching and vector space models with link-based ranking methods is demonstrated. The PageRank algorithm is introduced, and its numerical and spectral properties are discussed. The article concludes with an alternative means of computing PageRank, along with some example applications of this new method.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:12:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 14. Algorithms of the Copula Fit to the Nonlinear Processes in the Utility Industry Andrejs, Matveevs PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_13_j_idt606",{id:"formSmash:items:resultList:13:j_idt606",widgetVar:"widget_formSmash_items_resultList_13_j_idt606",onLabel:"Andrejs, Matveevs ",offLabel:"Andrejs, Matveevs ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_13_j_idt609",{id:"formSmash:items:resultList:13:j_idt609",widgetVar:"widget_formSmash_items_resultList_13_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Riga Technical University, Latvia.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:13:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fjodorovs, JegorsRiga Technical University, Latvia.Malyarenko, AnatoliyMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:13:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Algorithms of the Copula Fit to the Nonlinear Processes in the Utility Industry2017In: Procedia Computer Science, E-ISSN 1877-0509, Vol. 104, p. 572-577Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_13_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:13:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_13_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Our research studies the construction and estimation of copula-based semi parametric Markov model for the processes, which involved in water flows in the hydro plants. As a rule analyzing the dependence structure of stationary time series regressive models defined by invariant marginal distributions and copula functions that capture the temporal dependence of the processes is considered. This permits to separate out the temporal dependence (such as tail dependence) from the marginal behavior (such as fat tails) of a time series. Dealing with utility company data we have found the best copula describing data - Gumbel copula. As a result constructed algorithm was used for an imitation of low probability events (in a hydro power industry) and predictions.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:13:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 15. Algorithms for recalculating alpha and eigenvector centrality measures using graph partitioning techniques Anguzu, Collins PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_14_j_idt606",{id:"formSmash:items:resultList:14:j_idt606",widgetVar:"widget_formSmash_items_resultList_14_j_idt606",onLabel:"Anguzu, Collins ",offLabel:"Anguzu, Collins ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_14_j_idt609",{id:"formSmash:items:resultList:14:j_idt609",widgetVar:"widget_formSmash_items_resultList_14_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:14:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Engström, ChristopherMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Kasumba, HenryDepartment of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.Mango, John MageroDepartment of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:14:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Algorithms for recalculating alpha and eigenvector centrality measures using graph partitioning techniques2022In:*Springer Proceedings in Mathematics and Statistics*, Springer Nature, 2022, Vol. 408, p. 541-562Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_14_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:14:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_14_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In graph theory, centrality measures are very crucial in ranking vertices of the graph in order of their importance. Alpha and eigenvector centralities are some of the highly placed centrality measures applied especially in social network analysis, disease diffusion networks and mechanical infrastructural developments. In this study we focus on recalculating alpha and eigenvector centralities using graph partitioning techniques. We write an algorithm for partitioning, sorting and efficiently computing these centralities for a graph. We then numerically demonstrate the technique on some sample small-sized networks to recalculate the two centrality measures

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:14:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 16. A Comparison of Graph Centrality Measures Based on Lazy Random Walks Anguzu, Collins PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_15_j_idt606",{id:"formSmash:items:resultList:15:j_idt606",widgetVar:"widget_formSmash_items_resultList_15_j_idt606",onLabel:"Anguzu, Collins ",offLabel:"Anguzu, Collins ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_15_j_idt609",{id:"formSmash:items:resultList:15:j_idt609",widgetVar:"widget_formSmash_items_resultList_15_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematics, Makerere University, Kampala, Uganda.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:15:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Engström, ChristopherMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:15:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A Comparison of Graph Centrality Measures Based on Lazy Random Walks2021In: Applied Modeling Techniquesand Data Analysis 1: Computational Data AnalysisMethods and Tools / [ed] Yannis Dimotikalis, Alex Karagrigoriou, Christina Parpoula, Christos H Skiadas, John Wiley & Sons, Inc. Hoboken, NJ, USA , 2021, Vol. 7, p. 91-111Chapter in book (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_15_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:15:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_15_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); When working with a network, it is often of interest to locate the “most important”nodes in the network. A common way to do this is by using some graph centralitymeasures. Since what constitutes as an important node varies from one network toanother, or even in applications on the same network, there is a large number ofdifferent centrality measures proposed in the literature. Due to the large amount ofdifferent centrality measures proposed in different fields, there is also a large amountof very similar or equivalent centrality measures (in the sense that they give the sameranks). In this chapter, we focus on the centrality measures based on powers of theadjacency matrix and those based on random walk. In this case, we show how someof these centrality measures are related, as well as their lazy variants.We will performsome experiments to demonstrate the similarities between the centrality measures.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:15:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 17. A comparison of graph centrality measures based on random walks and their computation Anguzu, Collins PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_16_j_idt606",{id:"formSmash:items:resultList:16:j_idt606",widgetVar:"widget_formSmash_items_resultList_16_j_idt606",onLabel:"Anguzu, Collins ",offLabel:"Anguzu, Collins ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_16_j_idt609",{id:"formSmash:items:resultList:16:j_idt609",widgetVar:"widget_formSmash_items_resultList_16_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:16:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Engström, ChristopherMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:16:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A comparison of graph centrality measures based on random walks and their computation2019In: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019 / [ed] Christos H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2019, p. 121-135Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_16_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:16:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_16_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); When working with a network it is often of interest to locate the "most important" nodes in the network. A common way to do this is using some graph centrality measures. Since what constitutes an important node is different between different networks or even applications on the same network there is a large amount of different centrality measures proposed in the literature. Due to the large amount of different centrality measures proposed in different fields, there is also a large amount very similar or equivalent centrality measures in the sense that they give the same ranks. In this paper we will focus on centrality measures based on powers of the adjacency matrix or similar matrices and those based on random walk in order to show how some of these are related and can be calculated efficiently using the same or slightly altered algorithms.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:16:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 18. Calibration of Multiscale Two-Factor Stochastic Volatility Models: A Second-Order Asymptotic Expansion Approach Betuel, Canhanga PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_17_j_idt606",{id:"formSmash:items:resultList:17:j_idt606",widgetVar:"widget_formSmash_items_resultList_17_j_idt606",onLabel:"Betuel, Canhanga ",offLabel:"Betuel, Canhanga ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_17_j_idt609",{id:"formSmash:items:resultList:17:j_idt609",widgetVar:"widget_formSmash_items_resultList_17_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Faculty of Sciences, Dept of Mathematics and Computer Sciences, Eduardo Mondlane University, Mozambique.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:17:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Malyarenko, AnatoliyMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Ni, YingMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Rancic, MilicaMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:17:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Calibration of Multiscale Two-Factor Stochastic Volatility Models: A Second-Order Asymptotic Expansion Approach2018In: / [ed] Christos H Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2018Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_17_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:17:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_17_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The development of financial markets imposes more complex models on the option pricing problems. On the previous papers by the authors, we consider a model under which the underlying asset is driven by two independent Heston-type stochastic volatility processes of multiscale (fast and slow) mean-reverting rates and we compute an approximate solution for the option pricing problem, using asymptotic expansion method. In the present paper, we aim to calibrate the model using the market prices of options on Euro Stoxx 50 index and an equity stock in the European market. Our approach is to use the market implied volatility surface for calibrating directly a set of new parameters required in our second-order asymptotic expansion pricing formula for European options. This secondorder asymptotic expansion formula provides a better approximation formula for European option prices than the first-order formula, as explained in an earlier work of the authors.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:17:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 19. Monte Carlo semi-Markov methods for credit risk migration and Basel II rules II Biffi, Elenaet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_18_j_idt609",{id:"formSmash:items:resultList:18:j_idt609",widgetVar:"widget_formSmash_items_resultList_18_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:18:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); D'Amico, GuillermoDi Biase, GJanssen, JManca, RaimondoSilvestrov, DmitriiMälardalen University, School of Education, Culture and Communication.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:18:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Monte Carlo semi-Markov methods for credit risk migration and Basel II rules II2008In: Journal of Numerical and Applied Mathematics, Vol. 96, p. 59-86Article in journal (Refereed)20. Monte Carlo semi-Markov methods for credit risk migration and Basel II rules. I. Biffi, Elenaet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_19_j_idt609",{id:"formSmash:items:resultList:19:j_idt609",widgetVar:"widget_formSmash_items_resultList_19_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:19:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); D'Amigo, GuillermoDi Biase, GiuseppeJanssen, JacquesManca, RaimondoSilvestrov, DmitriiMälardalen University, School of Education, Culture and Communication.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:19:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Monte Carlo semi-Markov methods for credit risk migration and Basel II rules. I.2008In: Journal of Numerical and Applied Mathematics, ISSN 0868-6912, Vol. 1, p. 28-58Article in journal (Refereed)21. Exploring The Relationship Between Ordinary PageRank, Lazy PageRank and Random Walk with Backstep PageRank for Different Graph Structures Biganda, Pitos PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_20_j_idt606",{id:"formSmash:items:resultList:20:j_idt606",widgetVar:"widget_formSmash_items_resultList_20_j_idt606",onLabel:"Biganda, Pitos ",offLabel:"Biganda, Pitos ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_20_j_idt609",{id:"formSmash:items:resultList:20:j_idt609",widgetVar:"widget_formSmash_items_resultList_20_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:20:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Abola, BenardMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.Engström, ChristopherMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Mango, John MageroDepartment of Mathematics, Makerere University, Uganda.Kakuba, GodwinDepartment of Mathematics, Makerere University, Uganda.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:20:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Exploring The Relationship Between Ordinary PageRank, Lazy PageRank and Random Walk with Backstep PageRank for Different Graph Structures2020In: Data Analysis and Applications 3: Computational, Classification, Financial, Statistical and Stochastic Methods, Volume 5 / [ed] A. Makrides, A. Karagrigoriou, C.H. Skiadas, John Wiley & Sons, Ltd , 2020, p. 53-73Chapter in book (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_20_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:20:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_20_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PageRank is an algorithm for ranking web pages. It is the first and best known webgraph-based algorithm in the Google search engine. The algorithm is simple, robust and reliable to measure the importance of web pages. This chapter presents a comparative review of three variants of PageRank, namely ordinary PageRank (introduced by Brin and Page as a measure of importance of a web page), lazy PageRank and random walk with backstep PageRank. It compares the variants in terms of their convergence and consistency in rank scores for different graph structures with reference to PageRank’s parameters, damping factor and backstep parameter. The chapter also shows that ordinary PageRank can be formulated from the other two variants by some proportionality relationships.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:20:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 22. Traditional and lazy pageranks for a line of nodes connected with complete graphs Biganda, Pitos PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_21_j_idt606",{id:"formSmash:items:resultList:21:j_idt606",widgetVar:"widget_formSmash_items_resultList_21_j_idt606",onLabel:"Biganda, Pitos ",offLabel:"Biganda, Pitos ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_21_j_idt609",{id:"formSmash:items:resultList:21:j_idt609",widgetVar:"widget_formSmash_items_resultList_21_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:21:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Abola, BenardMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.Engström, ChristopherMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Mango, John MageroDepartment of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.Kakuba, GodwinDepartment of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:21:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Traditional and lazy pageranks for a line of nodes connected with complete graphs2018In: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Springer, 2018, Vol. 271, p. 391-412Chapter in book (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_21_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:21:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_21_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PageRank was initially defined by S. Brin and L. Page for the purpose of measuring the importance of web pages (nodes) based on the structure of links between them. Due to existence of diverse methods of random walk on the graph, variants of PageRank now exists. They include traditional (or normal) PageRank due to normal random walk and Lazy PageRank due to lazy random walk on a graph. In this article, we establish how the two variants of PageRank changes when complete graphs are connected to a line of nodes whose links between the nodes are in one direction. Explicit formulae for the two variants of PageRank are presented. We have noted that the ranks on a line graph are the same except their numerical values which differ. Further, we have observed that both normal random walk and lazy random walk on complete graphs spend almost the same time at each node.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:21:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 23. PageRank and perturbed Markov chains Biganda, Pitos PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_22_j_idt606",{id:"formSmash:items:resultList:22:j_idt606",widgetVar:"widget_formSmash_items_resultList_22_j_idt606",onLabel:"Biganda, Pitos ",offLabel:"Biganda, Pitos ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_22_j_idt609",{id:"formSmash:items:resultList:22:j_idt609",widgetVar:"widget_formSmash_items_resultList_22_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:22:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Abola, BenardMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.Engström, ChristopherMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Mango, John MageroDepartment of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.Kakuba, GudwinDepartment of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:22:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PageRank and perturbed Markov chains2019In: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019 / [ed] Christos H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2019, p. 233-247Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_22_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:22:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_22_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PageRank is a widely-used hyperlink-based algorithm to estimate the relative importance of nodes in networks [11]. Since many real world networks are large sparse networks, this makes efficient calculation of PageRank complicated. Moreover, one needs to escape from dangling effects in some cases as well as slow convergence of the transition matrix. Primitivity adjustment with a damping (perturbation) parameter ε(0,ε

_{0}] (for fixed ε_{0 }0.15) is one of the essential procedure that is known to ensure convergence of the transition matrix [24]. If ε is large, the transition matrix looses information due to shift of information to teleportation matrix [27]. In this paper, we formulate PageRank problem as the first and second order Markov chains perturbation problem. Using numerical experiments, we compare convergence rates for the two problems for different values of ε on different graph structures and investigate the difference in ranks for the two problems.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:22:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 24. PageRank and Perturbed Markov Chains Biganda, Pitos PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_23_j_idt606",{id:"formSmash:items:resultList:23:j_idt606",widgetVar:"widget_formSmash_items_resultList_23_j_idt606",onLabel:"Biganda, Pitos ",offLabel:"Biganda, Pitos ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_23_j_idt609",{id:"formSmash:items:resultList:23:j_idt609",widgetVar:"widget_formSmash_items_resultList_23_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:23:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Abola, BenardMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.Engström, ChristopherMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Kakuba, GodwinDepartment of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.Mango, John MageroDepartment of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:23:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PageRank and Perturbed Markov Chains2021In: Applied Modeling Techniques and Data Analysis 1: Computational Data Analysis Methods and Tools / [ed] Yannis Dimotikalis, Alex Karagrigoriou, Christina Parpoula, Christos H. Skiadas, John Wiley & Sons, Inc. Hoboken, NJ, USA , 2021, Vol. 7, p. 57-74Chapter in book (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_23_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:23:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_23_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PageRank is a widely used hyperlink-based algorithm for estimating the relative importance of nodes in networks. Since many real-world networks are large sparse networks, efficient calculation of PageRank is complicated. Moreover, we need to overcome dangling effects in some cases as well as slow convergence of the transition matrix. Primitivity adjustment with a damping (perturbation) parameter is one of the essential procedures known to ensure convergence of the transition matrix. If the perturbation parameter is not small enough, the transition matrix loses information due to the shift of information to the teleportation matrix. We formulate the PageRank problem as a first- and second-order Markov chains perturbation problem. Using numerical experiments, we compare convergence rates for different values of perturbation parameter on different graph structures and investigate the difference in ranks for the two problems.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:23:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 25. Analysis of Key Comparisons with Two Reference Standards Bodnar, Olha PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_24_j_idt606",{id:"formSmash:items:resultList:24:j_idt606",widgetVar:"widget_formSmash_items_resultList_24_j_idt606",onLabel:"Bodnar, Olha ",offLabel:"Bodnar, Olha ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Physikalisch-Technische Bundesanstalt, Berlin, Germany.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:24:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:24:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Analysis of Key Comparisons with Two Reference Standards: Extended Random Effects Meta-Analysis2018In: Advanced Mathematical and Computational Tools in Metrology and Testing XI / [ed] Alistair B Forbes; Nien-Fan Zhang; Anna Chunovkina; Sascha Eichstädt, Singapore: World Scientific, 2018, p. 1-8Chapter in book (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_24_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:24:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_24_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We propose a statistical method for analyzing key comparisons with two transfer standards measured in two petals. The new approach is based on an extension of the established random effects model. A full Bayesian analysis based on the reference prior is developed and analytic expressions for the results are derived. One benefit of the suggested approach is that it provides a comprehensive assessment of the laboratory biases in terms of their posterior distributions. Another advantage is that it can easily be applied in practice. The approach is illustrated for the CCM.M-K7 key comparison data.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:24:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 26. Assessment of Vague and Noninformative Priors for Bayesian Estimation of the Realized Random Effects in Random Effects Meta-Analysis Bodnar, Olha PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_25_j_idt606",{id:"formSmash:items:resultList:25:j_idt606",widgetVar:"widget_formSmash_items_resultList_25_j_idt606",onLabel:"Bodnar, Olha ",offLabel:"Bodnar, Olha ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_25_j_idt609",{id:"formSmash:items:resultList:25:j_idt609",widgetVar:"widget_formSmash_items_resultList_25_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Physikalisch-Technische Bundesanstalt, Germany.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:25:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Elster, ClemensPhysikalisch-Technische Bundesanstalt, Germany.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:25:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Assessment of Vague and Noninformative Priors for Bayesian Estimation of the Realized Random Effects in Random Effects Meta-Analysis2018In: AStA Advances in Statistical Analysis, ISSN 1863-8171, E-ISSN 1863-818X, Vol. 102, p. 1-20Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_25_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:25:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_25_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Random-effects meta-analysis has become a well-established tool applied in many areas, for example, when combining the results of several clinical studies on a treatment effect. Typically, the inference aims at the common mean and the amount of heterogeneity. In some applications, the laboratory effects are of interest, for example, when assessing uncertainties quoted by laboratories participating in an interlaboratory comparison in metrology. We consider the Bayesian estimation of the realized random effects in random-effects meta-analysis. Several vague and noninformative priors are examined as well as a proposed novel one. Conditions are established that ensure propriety of the posteriors for the realized random effects. We present extensive simulation results that assess the inference in dependence on the choice of prior as well as mis-specifications in the statistical model. Overall good performance is observed for all priors with the novel prior showing the most promising results. Finally, the uncertainties reported by eleven national metrology institutes and universities for their measurements on the Newtonian constant of gravitation are assessed.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:25:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 27. Robust Bayesian Linear Regression with Application to an Analysis of the CODATA Values for the Planck Constant Bodnar, Olha PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_26_j_idt606",{id:"formSmash:items:resultList:26:j_idt606",widgetVar:"widget_formSmash_items_resultList_26_j_idt606",onLabel:"Bodnar, Olha ",offLabel:"Bodnar, Olha ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_26_j_idt609",{id:"formSmash:items:resultList:26:j_idt609",widgetVar:"widget_formSmash_items_resultList_26_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Physikalisch-Technische Bundesanstalt, Germany.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:26:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Elster, ClemensPhysikalisch-Technische Bundesanstalt, Germany.Wübbeler, GerdPhysikalisch-Technische Bundesanstalt, Germany.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:26:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Robust Bayesian Linear Regression with Application to an Analysis of the CODATA Values for the Planck Constant2017In: Metrologia, ISSN 0026-1394, E-ISSN 1681-7575, Vol. 55, no 1, p. 20-28Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_26_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:26:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_26_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Weighted least-squares estimation is commonly applied in metrology to fit models to measurements that are accompanied with quoted uncertainties. The weights are chosen in dependence on the quoted uncertainties. However, when data and model are inconsistent in view of the quoted uncertainties, this procedure does not yield adequate results.

When it can be assumed that all uncertainties ought to be rescaled by a common factor, weighted least-squares estimation may still be used, provided that a simple correction of the uncertainty obtained for the estimated model is applied. We show that these uncertainties and credible intervals are robust, as they do not rely on the assumption of a Gaussian distribution of the data. Hence, common software for weighted least-squares estimation may still safely be employed in such a case, followed by a simple modification of the uncertainties obtained by that software. We also provide means of checking the assumptions of such an approach.

The Bayesian regression procedure is applied to analyze the CODATA values for the Planck constant published over the past decades in terms of three different models: a constant model, a straight line model and a spline model. Our results indicate that the CODATA values may not have yet stabilized

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:26:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 28. Approximate Bayesian Evaluations of Measurement Uncertainty Bodnar, Olha PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_27_j_idt606",{id:"formSmash:items:resultList:27:j_idt606",widgetVar:"widget_formSmash_items_resultList_27_j_idt606",onLabel:"Bodnar, Olha ",offLabel:"Bodnar, Olha ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_27_j_idt609",{id:"formSmash:items:resultList:27:j_idt609",widgetVar:"widget_formSmash_items_resultList_27_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:27:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Possolo, AntonioNational Institute of Standards and Technology, USA.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:27:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Approximate Bayesian Evaluations of Measurement Uncertainty2018Conference paper (Other academic)29. Approximate Bayesian evaluations of measurement uncertainty Bodnar, Olha PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_28_j_idt606",{id:"formSmash:items:resultList:28:j_idt606",widgetVar:"widget_formSmash_items_resultList_28_j_idt606",onLabel:"Bodnar, Olha ",offLabel:"Bodnar, Olha ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_28_j_idt609",{id:"formSmash:items:resultList:28:j_idt609",widgetVar:"widget_formSmash_items_resultList_28_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:28:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Possolo, AntonioNational Institute of Standards and Technology, USA.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:28:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Approximate Bayesian evaluations of measurement uncertainty2018In: Metrologia, ISSN 0026-1394, E-ISSN 1681-7575, Vol. 55, p. 147-157Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_28_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:28:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_28_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The

*Guide to the Expression of Uncertainty in Measurement*(GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty.This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand.

The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists.

We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:28:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 30. Application of a power-exponential function-based model to mortality rates forecasting Boulougari, Andromachiet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_29_j_idt609",{id:"formSmash:items:resultList:29:j_idt609",widgetVar:"widget_formSmash_items_resultList_29_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:29:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Lundengård, KarlMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Rancic, MilicaMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Strass, BelindaSuleiman, SamyaMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. University of Dar es salaam, Dar es salaam, Tanzania.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:29:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Application of a power-exponential function-based model to mortality rates forecasting2019In: Communications in Statistics: Case Studies, Data Analysis and Applications, E-ISSN 2373-7484, Vol. 5, no 1, p. 3-10Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_29_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:29:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_29_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); There are many models for mortality rates. A well-known problem that complicates modeling of human mortality rates is the “accident hump” occurring in early adulthood. Here, two models of mortality rate based on power-exponential functions are presented and compared to a few other models. The models will be fitted to known data of measured death rates from several different countries using numerical techniques for curve-fitting with the nonlinear least-squares method. The properties of the model with respect to forecasting with the Lee–Carter method will be discussed.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:29:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 31. Benford’s Law: Analysis of the trustworthiness of COVID-19 reporting in the context of different political regimes Burlac, Leonid PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_30_j_idt606",{id:"formSmash:items:resultList:30:j_idt606",widgetVar:"widget_formSmash_items_resultList_30_j_idt606",onLabel:"Burlac, Leonid ",offLabel:"Burlac, Leonid ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_30_j_idt609",{id:"formSmash:items:resultList:30:j_idt609",widgetVar:"widget_formSmash_items_resultList_30_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Mälardalen University, School of Education, Culture and Communication.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:30:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Giannakis, NikolaosMälardalen University, School of Education, Culture and Communication.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:30:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Benford’s Law: Analysis of the trustworthiness of COVID-19 reporting in the context of different political regimes2021Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAbstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_30_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:30:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_30_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In order for governments and demographers to, among other things, design policies and pensionplans, as well as for insurance companies to offer policies that serve general public, having reliable mortality data plays a crucial role. The academic world works actively in developing tools (models and methods) that can, based on collected mortality data, forecast future death rates in the observed population. Obviously, to be able to rely on the predicated data one needs a reliable source of existing mortality data. In the light of the ongoing COVID-19 pandemic, reliability of certain death-case reporting has been questioned. In this thesis, the Benford’s Law is used to evaluate how well countries with authoritarian regimes (Azerbaijan, Belarus),and with democratic regimes (Greece, Serbia, Sweden), report their COVID-19 cases to theworldwide public. Statistical tests such as the Chi-squared test, mean absolute deviation, and the distribution distance were used to obtain the results needed to form our conclusions. During our testing, we found that countries with democratic regimes do conform better to the Benford’s law than the authoritarian ones.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:30:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_30_j_idt869_0_j_idt872",{id:"formSmash:items:resultList:30:j_idt869:0:j_idt872",widgetVar:"widget_formSmash_items_resultList_30_j_idt869_0_j_idt872",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:30:j_idt869:0:fullText"});}); 32. Advanced Monte Carlo pricing of european options in a market model with two stochastic volatilities Canhanga, Betuel PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_31_j_idt606",{id:"formSmash:items:resultList:31:j_idt606",widgetVar:"widget_formSmash_items_resultList_31_j_idt606",onLabel:"Canhanga, Betuel ",offLabel:"Canhanga, Betuel ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_31_j_idt609",{id:"formSmash:items:resultList:31:j_idt609",widgetVar:"widget_formSmash_items_resultList_31_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Eduardo Mondlane University, Maputo, Mozambique.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:31:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Malyarenko, AnatoliyMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Murara, Jean-PaulMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Ni, YingMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:31:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Advanced Monte Carlo pricing of european options in a market model with two stochastic volatilities2020In: Algebraic Structures and Applications / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rancic, Springer Nature, 2020, Vol. 317, p. 857-874Chapter in book (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_31_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:31:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_31_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We consider a market model with four correlated factors and two stochastic volatilities, one of which is rapid-changing, while another one is slow-changing in time. An advanced Monte Carlo method based on the theory of cubature in Wiener space is used to find the no-arbitrage price of the European call option in the above model.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:31:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 33. Numerical Studies on Asymptotics of European Option under Multiscale Stochastic Volatility Canhanga, Betuel PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_32_j_idt606",{id:"formSmash:items:resultList:32:j_idt606",widgetVar:"widget_formSmash_items_resultList_32_j_idt606",onLabel:"Canhanga, Betuel ",offLabel:"Canhanga, Betuel ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_32_j_idt609",{id:"formSmash:items:resultList:32:j_idt609",widgetVar:"widget_formSmash_items_resultList_32_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:32:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Malyarenko, AnatoliyMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Murara, Jean-PaulMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Ni, YingMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:32:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Numerical Studies on Asymptotics of European Option under Multiscale Stochastic Volatility2015In: ASMDA 2015 Proceedings: 16th Applied Stochastic Models and Data Analysis International Conference with 4th Demographics 2015 Workshop / [ed] Christos H Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2015, p. 53-66Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_32_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:32:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_32_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Multiscale stochastic volatilities models relax the constant volatility assumption from Black-Scholes option pricing model. Such model can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. Christoffersen et al. [3] presented a model where the underlying priceis governed by two volatility components, one changing fast and another changing slowly. Chiarella and Ziveyi [2] transformed Christoffersen’s model and computed an approximate formula for pricing American options. They used Duhamel’s principle to derive an integral form solution of the boundary value problem associated to the option price. Using method of characteristics, Fourier and Laplace transforms, they obtained with good accuracy the American options prices. In a previous research of the authors (Canhanga et al. [1]), a particular case of Chiarella and Ziveyi [2] model is used for pricing of European options. The novelty of this earlier work is to present an asymptotic expansion for the option price. The present paper provides experimental and numerical studies on investigating the accuracy of the approximation formulae given by this asymptotic expansion. We present also a procedure for calibrating the parameters produced by our first-order asymptotic approximation formulae. Our approximated option prices will be compared to the approximation obtained by Chiarella and Ziveyi [2].

1. Canhanga B., Malyarenko, A., Ni, Y. and Silvestrov S. Perturbation methods for pricing European options in a model with two stochastic volatilities. 3rd SMTDA Conference Proceedings. 11-14 June 2014, Lisbon Porturgal, C. H. Skiadas (Ed.) 489-500 (2014).

2. Chiarella, C, and Ziveyi, J. American option pricing under two stochastic volatility processes. J. Appl. Math. Comput. 224:283–310 (2013).

3. Christoffersen, P.; Heston, S.; Jacobs, K. The shape and term structure of the index option smirk: why multifactor stochastic volatility models work so well. Manage. Sci. 55 (2) 1914-1932; (2009).

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:32:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 34. Numerical Studies on Asymptotics of European Option Under Multiscale Stochastic Volatility Canhanga, Betuel PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_33_j_idt606",{id:"formSmash:items:resultList:33:j_idt606",widgetVar:"widget_formSmash_items_resultList_33_j_idt606",onLabel:"Canhanga, Betuel ",offLabel:"Canhanga, Betuel ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_33_j_idt609",{id:"formSmash:items:resultList:33:j_idt609",widgetVar:"widget_formSmash_items_resultList_33_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); DMI, Eduardo Mondlane University, Maputo, Mozambique.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:33:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Malyarenko, AnatoliyMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Murara, Jean-PaulMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Ni, YingMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:33:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Numerical Studies on Asymptotics of European Option Under Multiscale Stochastic Volatility2017In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 19, no 4, p. 1075-1087Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_33_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:33:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_33_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Multiscale stochastic volatilities models relax the constant volatility assumption from Black-Scholes option pricing model. Such models can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. Christoffersen et al. Manag Sci 55(2):1914–1932 (2009) presented a model where the underlying price is governed by two volatility components, one changing fast and another changing slowly. Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) transformed Christoffersen’s model and computed an approximate formula for pricing American options. They used Duhamel’s principle to derive an integral form solution of the boundary value problem associated to the option price. Using method of characteristics, Fourier and Laplace transforms, they obtained with good accuracy the American option prices. In a previous research of the authors (Canhanga et al. 2014), a particular case of Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) model is used for pricing of European options. The novelty of this earlier work is to present an asymptotic expansion for the option price. The present paper provides experimental and numerical studies on investigating the accuracy of the approximation formulae given by this asymptotic expansion. We present also a procedure for calibrating the parameters produced by our first-order asymptotic approximation formulae. Our approximated option prices will be compared to the approximation obtained by Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013).

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:33:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 35. Pricing European Options Under Stochastic Volatilities Models Canhanga, Betuel PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_34_j_idt606",{id:"formSmash:items:resultList:34:j_idt606",widgetVar:"widget_formSmash_items_resultList_34_j_idt606",onLabel:"Canhanga, Betuel ",offLabel:"Canhanga, Betuel ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_34_j_idt609",{id:"formSmash:items:resultList:34:j_idt609",widgetVar:"widget_formSmash_items_resultList_34_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:34:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Malyarenko, AnatoliyMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Murara, Jean-PaulMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:34:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Pricing European Options Under Stochastic Volatilities Models2016In: Engineering Mathematics I: Electromagnetics, Fluid Mechanics, Material Physics and Financial Engineering / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016, p. 315-338Chapter in book (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_34_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:34:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_34_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Interested by the volatility behavior, different models have been developed for option pricing. Starting from constant volatility model which did not succeed on capturing the effects of volatility smiles and skews; stochastic volatility models appearas a response to the weakness of the constant volatility models. Constant elasticity of volatility, Heston, Hull and White, Schöbel-Zhu, Schöbel-Zhu-Hull-Whiteand many others are examples of models where the volatility is itself a random process. Along the chapter we deal with this class of models and we present the techniques of pricing European options. Comparing single factor stochastic volatility models to constant factor volatility models it seems evident that the stochastic volatility models represent nicely the movement of the asset price and its relations with changes in the risk. However, these models fail to explain the large independent fluctuations in the volatility levels and slope. Christoffersen et al. in [4] proposed a model with two-factor stochastic volatilities where the correlation between the underlying asset price and the volatilities varies randomly. In the last section of this chapter we introduce a variation of Chiarella and Ziveyi model, which is a subclass of the model presented in [4] and we use the first order asymptotic expansion methods to determine the price of European options.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:34:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 36. Analytical and Numerical Studies on the Second Order Asymptotic Expansion Method for European Option Pricing under Two-factor Stochastic Volatilities Canhanga, Betuel PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_35_j_idt606",{id:"formSmash:items:resultList:35:j_idt606",widgetVar:"widget_formSmash_items_resultList_35_j_idt606",onLabel:"Canhanga, Betuel ",offLabel:"Canhanga, Betuel ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_35_j_idt609",{id:"formSmash:items:resultList:35:j_idt609",widgetVar:"widget_formSmash_items_resultList_35_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Faculty of Sciences, Department of Mathematics and Computer Sciences, Eduardo Mondlane University, Maputo, Mozambique.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:35:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Malyarenko, AnatoliyMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Ni, YingMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Rancic, MilicaMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:35:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Analytical and Numerical Studies on the Second Order Asymptotic Expansion Method for European Option Pricing under Two-factor Stochastic Volatilities2018In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 47, no 6, p. 1328-1349Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_35_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:35:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_35_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The celebrated Black–Scholes model made the assumption of constant volatility but empirical studies on implied volatility and asset dynamics motivated the use of stochastic volatilities. Christoffersen in 2009 showed that multi-factor stochastic volatilities models capture the asset dynamics more realistically. Fouque in 2012 used it to price European options. In 2013 Chiarella and Ziveyi considered Christoffersen's ideas and introduced an asset dynamics where the two volatilities of the Heston type act separately and independently on the asset price, and using Fourier transform for the asset price process and double Laplace transform for the two volatilities processes, solved a pricing problem for American options. This paper considers the Chiarella and Ziveyi model and parameterizes it so that the volatilities revert to the long-run-mean with reversion rates that mimic fast(for example daily) and slow(for example seasonal) random effects. Applying asymptotic expansion method presented by Fouque in 2012, we make an extensive and detailed derivation of the approximation prices for European options. We also present numerical studies on the behavior and accuracy of our first and the second order asymptotic expansion formulas.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:35:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 37. Perturbation Methods for Pricing European Options in a Model with Two Stochastic Volatilities Canhanga, Betuel PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_36_j_idt606",{id:"formSmash:items:resultList:36:j_idt606",widgetVar:"widget_formSmash_items_resultList_36_j_idt606",onLabel:"Canhanga, Betuel ",offLabel:"Canhanga, Betuel ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_36_j_idt609",{id:"formSmash:items:resultList:36:j_idt609",widgetVar:"widget_formSmash_items_resultList_36_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:36:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Malyarenko, AnatoliyMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Ni, YingMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:36:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Perturbation Methods for Pricing European Options in a Model with Two Stochastic Volatilities2015In: New trends in Stochastic Modeling and Data Analysis, ISAST , 2015, p. 199-210Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_36_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:36:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_36_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Financial models have to reflect the characteristics of markets in which they are developed to be able to predict the future behavior of a financial system. The nature of most trading environments is characterized by uncertainties which are expressed in mathematical models in terms of volatilities. In contrast to the classical Black-Scholes model with constant volatility, our model includes one fast-changing and another slow-changing stochastic volatilities of mean-reversion type. The different changing frequencies of volatilities can be interpreted as the effects of weekends and effects of seasons of the year (summer and winter) on the asset price.

We perform explicitly the transition from the real-world to the risk-neutral probability measure by introducing market prices of risk and applying Girsanov Theorem. To solve the boundary value problem for the partial differential equation that corresponds to the case of a European option, we perform both regular and singular multiscale expansions in fractional powers of the speed of mean-reversion factors. We then construct an approximate solution given by the two-dimensional Black-Scholes model plus some terms that expand the results obtained by Black and Scholes.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:36:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 38. Numerical Methods on European Options Second Order Asymptotic Expansions for Multiscale Stochastic Volatility Canhanga, Betuel PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_37_j_idt606",{id:"formSmash:items:resultList:37:j_idt606",widgetVar:"widget_formSmash_items_resultList_37_j_idt606",onLabel:"Canhanga, Betuel ",offLabel:"Canhanga, Betuel ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_37_j_idt609",{id:"formSmash:items:resultList:37:j_idt609",widgetVar:"widget_formSmash_items_resultList_37_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:37:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Ni, YingMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Rancic, MilicaMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Malyarenko, AnatoliyMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:37:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Numerical Methods on European Options Second Order Asymptotic Expansions for Multiscale Stochastic Volatility2017In: INCPAA 2016 Proceedings: 11th International Conference on Mathematical Problems in Engineering, Aerospace, and Sciences, ICNPAA 2016, La Rochelle, France, 4 - 8 July 2016. / [ed] S. Sivasundaram, 2017, Vol. 1798, p. 020035-1-020035-10, article id 020035Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_37_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:37:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_37_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); After Black-Scholes proposed a model for pricing European Option in 1973, Cox, Ross and Rubinstein in 1979, and Heston in 1993, showed that the constant volatility assumption in the Black-Scholes model was one of the main reasons for the model to be unable to capture some market details. Instead of constant volatilities, they introduced non-constant volatilities to the asset dynamic modeling. In 2009, Christoffersen empirically showed "why multi-factor stochastic volatility models work so well". Four years later, Chiarella and Ziveyi solved the model proposed by Christoffersen. They considered an underlying asset whose price is governed by two factor stochastic volatilities of mean reversion type. Applying Fourier transforms, Laplace transforms and the method of characteristics they presented an approximate formula for pricing American option.The huge calculation involved in the Chiarella and Ziveyi approach motivated us to investigate another approach to compute European option prices on a Christoffersen type model. Using the first and second order asymptotic expansion method we presented a closed form solution for European option, and provided experimental and numerical studies on investigating the accuracy of the approximation formulae given by the first order asymptotic expansion. In the present chapter we will perform experimental and numerical studies for the second order asymptotic expansion and compare the obtained results with results presented by Chiarella and Ziveyi.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:37:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 39. On the Approximation of Physiologically Structured Population Model with a Three Stage-Structured Population Model in a Grazing System Canpwonyi, S. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_38_j_idt606",{id:"formSmash:items:resultList:38:j_idt606",widgetVar:"widget_formSmash_items_resultList_38_j_idt606",onLabel:"Canpwonyi, S. ",offLabel:"Canpwonyi, S. ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_38_j_idt609",{id:"formSmash:items:resultList:38:j_idt609",widgetVar:"widget_formSmash_items_resultList_38_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematics, Gulu University, Gulu, Uganda.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:38:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Carlsson, LinusMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:38:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On the Approximation of Physiologically Structured Population Model with a Three Stage-Structured Population Model in a Grazing System2022In: Springer Proc. Math. Stat., Springer , 2022, p. 753-771Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_38_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:38:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_38_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); A great deal of ecological theory is based on simple Lotka-Volterra-type of unstructured population models in the study of complex population dynamics and communities. The main reason is to obtain important information for predicting their future evolution. In these unstructured models, it is assumed that all individuals in the population are identical, with the same birth and death rates, and consume equally from shared resources in a homogeneous environment. In reality, these assumptions are not biologically true but still forms a basis for modeling population ecology. We apply this paradigm on the grazing system consisting of coupled ordinary differential equations describing the dynamics of forage resource and livestock population in a grassland ecosystem. We do this by investigating the dynamics of the individuals at different life-history stages of juvenile and adult livestock. The mathematical derivation of the model is carried out to show how the physiologically structured population model can be approximated using a three stage-structured population model. Thus the resulting system of ordinary differential equations can be solved to predict density-dependent properties of the population since it provides a somewhat close-to-reality description of the natural and traditional grazing system. This model therefore certainly contains the needed information in the modeling methodology and accommodates the necessary amount of biological details about the population.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:38:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 40. Implied volatility with HJM–type Stochastic Volatility model Cap, Thi Diu PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_39_j_idt606",{id:"formSmash:items:resultList:39:j_idt606",widgetVar:"widget_formSmash_items_resultList_39_j_idt606",onLabel:"Cap, Thi Diu ",offLabel:"Cap, Thi Diu ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Mälardalen University, School of Education, Culture and Communication.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:39:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:39:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Implied volatility with HJM–type Stochastic Volatility model2021Independent thesis Advanced level (degree of Master (Two Years)), 28 HE creditsStudent thesisAbstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_39_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:39:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_39_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this thesis, we propose a new and simple approach of extending the single-factor Heston stochastic volatility model to a more flexible one in solving option pricing problems. In this approach, the volatility process for the underlying asset dynamics depends on the time to maturity of the option. As this idea is inspired by the Heath-Jarrow-Morton framework which models the evolution of the full dynamics of forward rate curves for various maturities, we name this approach as the HJM-type stochastic volatility (HJM-SV) model. We conduct an empirical analysis by calibrating this model to real-market option data for underlying assets including an equity (ABB stock) and a market index (EURO STOXX 50), for two separated time spans from Jan 2017 to Dec 2017 (before the COVID-19 pandemic) and from Nov 2019 to Nov 2020 (after the start of COVID-19 pandemic). We investigate the optimal way of dividing the set of option maturities into three classes, namely, the short-maturity, middle-maturity, and long-maturity classes. We calibrate our HJM-SV model to the data in the following way, for each class a single-factor Heston stochastic volatility model is calibrated to the corresponding market data. We address the question that how well the new HJM-SV model captures the feature of implied volatility surface given by the market data.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:39:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_39_j_idt869_0_j_idt872",{id:"formSmash:items:resultList:39:j_idt869:0:j_idt872",widgetVar:"widget_formSmash_items_resultList_39_j_idt869_0_j_idt872",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:39:j_idt869:0:fullText"});}); 41. Exploring the world of financial engineering Carkovs, Jevgenijs PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_40_j_idt606",{id:"formSmash:items:resultList:40:j_idt606",widgetVar:"widget_formSmash_items_resultList_40_j_idt606",onLabel:"Carkovs, Jevgenijs ",offLabel:"Carkovs, Jevgenijs ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_40_j_idt609",{id:"formSmash:items:resultList:40:j_idt609",widgetVar:"widget_formSmash_items_resultList_40_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Riga Technical University.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:40:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Malyarenko, AnatoliyMälardalen University, School of Education, Culture and Communication.Pärna, KalevUniversity of Tartu.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:40:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Exploring the world of financial engineering2011Collection (editor) (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_40_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:40:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_40_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Mälardalen University (Sweden), Riga Technical University (Latvia) and University of Tartu (Estonia) organised courses “Exploring the world of financial engineering" for teachers and students of the above higher education institutions under financial support of the Nordplus Framework mobility project HE-2010_1a-21005. These courses take place in the city of Västerås (Sweden) on May 9–May 13, 2011. In this book, we present the material of the courses’ lectures.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:40:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_40_j_idt869_0_j_idt872",{id:"formSmash:items:resultList:40:j_idt869:0:j_idt872",widgetVar:"widget_formSmash_items_resultList_40_j_idt869_0_j_idt872",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:40:j_idt869:0:fullText"});}); 42. From Constant to Rough Di Nunno, Giulia PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_41_j_idt606",{id:"formSmash:items:resultList:41:j_idt606",widgetVar:"widget_formSmash_items_resultList_41_j_idt606",onLabel:"Di Nunno, Giulia ",offLabel:"Di Nunno, Giulia ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_41_j_idt609",{id:"formSmash:items:resultList:41:j_idt609",widgetVar:"widget_formSmash_items_resultList_41_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Univ Oslo, Dept Math, N-0851 Oslo, Norway.;NHH Norwegian Sch Econ, Dept Business & Management Sci, N-5045 Bergen, Norway..PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:41:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Kubilius, KestutisVilnius Univ, Fac Math & Informat, LT-03225 Vilnius, Lithuania..Mishura, YuliiyaMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Taras Shevchenko Natl Univ Kyiv, Dept Probabil Stat & Actuarial Math, UA-01601 Kiev, Ukraine.Yurchenko-Tytarenko, AntonUniv Oslo, Dept Math, N-0851 Oslo, Norway..PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:41:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); From Constant to Rough: A Survey of Continuous Volatility Modeling2023In: Mathematics, E-ISSN 2227-7390, Vol. 11, no 19, article id 4201Article, review/survey (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_41_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:41:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_41_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this paper, we present a comprehensive survey of continuous stochastic volatility models, discussing their historical development and the key stylized facts that have driven the field. Special attention is dedicated to fractional and rough methods: without advocating for either roughness or long memory, we outline the motivation behind them and characterize some landmark models. In addition, we briefly touch on the problem of VIX modeling and recent advances in the SPX-VIX joint calibration puzzle.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:41:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 43. Numerical Studies of Implied Volatility Expansions Under the Gatheral Model Dimitrov, Marko PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_42_j_idt606",{id:"formSmash:items:resultList:42:j_idt606",widgetVar:"widget_formSmash_items_resultList_42_j_idt606",onLabel:"Dimitrov, Marko ",offLabel:"Dimitrov, Marko ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_42_j_idt609",{id:"formSmash:items:resultList:42:j_idt609",widgetVar:"widget_formSmash_items_resultList_42_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:42:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Albuhayri, MohammedMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Ni, YingMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Malyarenko, AnatoliyMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:42:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Numerical Studies of Implied Volatility Expansions Under the Gatheral Model2022In: Data Analysis and Related Applications 1: Computational, Algorithmic and Applied Economic Data Analysis / [ed] Konstantinos N. Zafeiris; Christos H. Skiadas; Yiannis Dimotikalis; Alex Karagrigoriou; Christiana Karagrigoriou-Vonta, London: ISTE Ltd , 2022, p. 135-148Chapter in book (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_42_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:42:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_42_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We calculate the price of the European call option in the Gatheral double stochastic volatility model by two independent methods. The first one is Monte Carlo simulation. For the second one, we use asymptotic expansions up to order 3 of the implied volatility in the above model calculated in our previous papers. We substitute the approximate value of the implied volatility to the Black--Scholes pricing formula. The results showing the accuracy of our approximation are presented.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:42:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 44. Properties of American options under a Markovian Regime Switching Model Dimitrov, Marko PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_43_j_idt606",{id:"formSmash:items:resultList:43:j_idt606",widgetVar:"widget_formSmash_items_resultList_43_j_idt606",onLabel:"Dimitrov, Marko ",offLabel:"Dimitrov, Marko ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_43_j_idt609",{id:"formSmash:items:resultList:43:j_idt609",widgetVar:"widget_formSmash_items_resultList_43_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:43:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Jin, LuUniversity of Electro-communications, Tokyo, Japan.Ni, YingMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:43:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Properties of American options under a Markovian Regime Switching Model: Properties of American options under a Markovian Regime Switching Model2021In: Communications in Statistics: Case Studies, Data Analysis and Applications, ISSN 2373-7484, Vol. 7, no 4, p. 573-589Article in journal (Refereed)Abstract [sv] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_43_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:43:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_43_j_idt644_0_j_idt645",onLabel:"Abstract [sv]",offLabel:"Abstract [sv]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this article, a model under which the underlying asset follows a Markov regime-switching process is considered. The underlying economy is partially observable in a form of a signal stochastically related to the actual state of the economy. The American option pricing problem is formulated using a partially observable Markov decision process (POMDP). Through the article, a three-state economy is assumed with a focus on the threshold for the early exercise, hold regions, and its monotonicity. An extensive numerical experimental study is conducted in order to clarify the relationship between the monotonicity of the exercising strategy and the sufficient conditions which are obtained in Jin, Dimitrov, and Ni. In this article, the effect of sufficient conditions is confirmed. It was shown that sufficient conditions are not necessary for the monotonicity of the exercising strategy, and a discussion including milder conditions is presented based on the numerical studies.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:43:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)DimitrovJinNi$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_43_j_idt869_0_j_idt872",{id:"formSmash:items:resultList:43:j_idt869:0:j_idt872",widgetVar:"widget_formSmash_items_resultList_43_j_idt869_0_j_idt872",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:43:j_idt869:0:fullText"});}); 45. Weak Convergence of First-Rare-Event Times for Semi-Markov Processes Drozdenko, Myroslav PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_44_j_idt606",{id:"formSmash:items:resultList:44:j_idt606",widgetVar:"widget_formSmash_items_resultList_44_j_idt606",onLabel:"Drozdenko, Myroslav ",offLabel:"Drozdenko, Myroslav ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Mälardalen University, Department of Mathematics and Physics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:44:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:44:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Weak Convergence of First-Rare-Event Times for Semi-Markov Processes2007Doctoral thesis, monograph (Other scientific)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_44_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:44:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_44_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this thesis we study necessary and sufficient conditions for weak convergence of first-rare-event times for semi-Markov processes, we describe the class of all possible limit distributions, and give the applications of the results to risk theory and queueing systems.

In paper

**A**, we consider first-rare-event times for semi-Markov processes with a finite set of states, and give a summary of our results concerning necessary and sufficient conditions for weak convergence of first-rare-event times and their actuarial applications.In paper

**B**, we present in detail results announced in paper**A**as well as their proofs. We give necessary and sufficient conditions for weak convergence of first-rare-event times for semi-Markov processes with a finite set of states in non-triangular-array mode and describe the class of all possible limit distributions in terms of their Laplace transforms.In paper

**C**, we study the conditions for weak convergence for flows of rare events for semi-Markov processes with a finite set of states in non-triangular array mode. We formulate necessary and sufficient conditions of convergence and describe the class of all possible limit stochastic flows. In the second part of the paper, we apply our results to the asymptotical analysis of non-ruin probabilities for perturbed risk processes.In paper

**D**, we give necessary and sufficient conditions for the weak convergence of first-rare-event times for semi-Markov processes with a finite set of states in triangular array mode as well as describing the class of all possible limit distributions. The results of paper**D**extend results obtained in paper**B**to a general triangular array mode.In paper

**E**, we give the necessary and sufficient conditions for weak convergence for the flows of rare events for semi-Markov processes with a finite set of states in triangular array case. This paper generalizes results obtained in paper**C**to a general triangular array mode. In the second part of the paper, we present applications of our results to asymptotical problems of perturbed risk processes and to queueing systems with quick servicePrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:44:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)FULLTEXT01$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_44_j_idt869_0_j_idt872",{id:"formSmash:items:resultList:44:j_idt869:0:j_idt872",widgetVar:"widget_formSmash_items_resultList_44_j_idt869_0_j_idt872",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:44:j_idt869:0:fullText"});}); 46. Comparison of Clustering Approaches through Their Application to Pharmacovigilance Terms Dupuch, Marie PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_45_j_idt606",{id:"formSmash:items:resultList:45:j_idt606",widgetVar:"widget_formSmash_items_resultList_45_j_idt606",onLabel:"Dupuch, Marie ",offLabel:"Dupuch, Marie ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_45_j_idt609",{id:"formSmash:items:resultList:45:j_idt609",widgetVar:"widget_formSmash_items_resultList_45_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); CNRS UMR 8163 STL, Universit´e Lille 3, 59653 Villeneuve d’Ascq, France.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:45:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Engström, ChristopherMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Hamon, ThierryLIM&BIO UFR SMBH Universit´e Paris 13, France.Grabar, NataliaCNRS UMR 8163 STL, Universit´e Lille 3, 59653 Villeneuve d’Ascq, France.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:45:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Comparison of Clustering Approaches through Their Application to Pharmacovigilance Terms2013In: Artificial Intelligence in Medicine. Lecture Notes in Computer Science, vol. 7885 / [ed] Niels Peek, Roque Marín Morales, Mor Peleg, Berlin Heidelberg: Springer, 2013, p. 58-67Chapter in book (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_45_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:45:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_45_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In different applications (i.e., information retrieval, filteringor analysis), it is useful to detect similar terms and to provide the possibilityto use them jointly. Clustering of terms is one of the methods whichcan be exploited for this. In our study, we propose to test three methodsdedicated to the clustering of terms (hierarchical ascendant classification,Radius and maximum), to combine them with the semantic distance algorithmsand to compare them through the results they provide whenapplied to terms from the pharmacovigilance area. The comparison indicatesthat the non disjoint clustering (Radius and maximum) outperformthe disjoint clusters by 10 to up to 20 points in all the experiments.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:45:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 47. Coupling and explicit rates of convergence in Cramér-Lundberg approximation for reinsurance risk processes Ekheden, Erhard PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_46_j_idt606",{id:"formSmash:items:resultList:46:j_idt606",widgetVar:"widget_formSmash_items_resultList_46_j_idt606",onLabel:"Ekheden, Erhard ",offLabel:"Ekheden, Erhard ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_46_j_idt609",{id:"formSmash:items:resultList:46:j_idt609",widgetVar:"widget_formSmash_items_resultList_46_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholm University.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:46:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Silvestrov, DmitriiStockholm University.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:46:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Coupling and explicit rates of convergence in Cramér-Lundberg approximation for reinsurance risk processes2011In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 40, no 19-20, p. 3524-3539Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_46_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:46:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_46_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); A classical result in risk theory is the Cramér-Lundberg approximation which says that under some general conditions the exponentially normalized ruin probability converges. In this article, we state an explicit rate of convergence for the Cramér-Lundberg approximation for ruin probabilities in the case where claims are bounded, which is realistic for, e.g., reinsurance models. The method, used to get the corresponding results, is based on renewal and coupling arguments.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:46:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 48. Generalisation of the Damping Factor in PageRank for Weighted Networks Engström, Christopher PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_47_j_idt606",{id:"formSmash:items:resultList:47:j_idt606",widgetVar:"widget_formSmash_items_resultList_47_j_idt606",onLabel:"Engström, Christopher ",offLabel:"Engström, Christopher ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_47_j_idt609",{id:"formSmash:items:resultList:47:j_idt609",widgetVar:"widget_formSmash_items_resultList_47_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:47:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:47:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Generalisation of the Damping Factor in PageRank for Weighted Networks2014In: Modern Problems in Insurance Mathematics / [ed] Silvestrov, Dmitrii; Martin-Löf, Anders, Springer International Publishing , 2014, p. 313-333Chapter in book (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_47_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:47:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_47_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this article we will look at the PageRank algorithm used to rank nodes in a network. While the method was originally used by Brin and Page to rank home pages in order of “importance”, since then many similar methods have been used for other networks such as financial or P2P networks. We will work with a non-normalised version of the usual PageRank definition which we will then generalise to enable better options, such as adapting the method or allowing more types of data. We will show what kind of effects the new options creates using examples as well as giving some thoughts on what it can be used for. We will also take a brief look at how adding new connections between otherwise unconnected networks can change the ranking.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:47:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 49. PageRank, a Look at Small Changes in a Line of Nodes and the Complete Graph Engström, Christopher PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_48_j_idt606",{id:"formSmash:items:resultList:48:j_idt606",widgetVar:"widget_formSmash_items_resultList_48_j_idt606",onLabel:"Engström, Christopher ",offLabel:"Engström, Christopher ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_48_j_idt609",{id:"formSmash:items:resultList:48:j_idt609",widgetVar:"widget_formSmash_items_resultList_48_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:48:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:48:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PageRank, a Look at Small Changes in a Line of Nodes and the Complete Graph2016In: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016, p. 223-247Chapter in book (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_48_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:48:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_48_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this article we will look at the PageRank algorithm used as part of the ranking process of different Internet pages in search engines by for example Google. This article has its main focus in the understanding of the behavior of PageRank as the system dynamically changes either by contracting or expanding such as when adding or subtracting nodes or links or groups of nodes or links. In particular we will take a look at link structures consisting of a line of nodes or a complete graph where every node links to all others. We will look at PageRank as the solution of a linear system of equations and do our examination in both the ordinary normalized version of PageRank as well as the non-normalized version found by solving corresponding linear system. We will show that using two different methods we can find explicit formulas for the PageRank of some simple link structures.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:48:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 50. PageRank, Connecting a Line of Nodes with a Complete Graph Engström, Christopher PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_49_j_idt606",{id:"formSmash:items:resultList:49:j_idt606",widgetVar:"widget_formSmash_items_resultList_49_j_idt606",onLabel:"Engström, Christopher ",offLabel:"Engström, Christopher ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_49_j_idt609",{id:"formSmash:items:resultList:49:j_idt609",widgetVar:"widget_formSmash_items_resultList_49_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:49:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:49:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PageRank, Connecting a Line of Nodes with a Complete Graph2016In: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016Chapter in book (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_49_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:49:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_49_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The focus of this article is the PageRank algorithm originally defined by S. Brin and L. Page as the stationary distribution of a certain random walk on a graph used to rank homepages on the Internet. We will attempt to get a better understanding of how PageRank changes after you make some changes to the graph such as adding or removing edge between otherwise disjoint subgraphs. In particular we will take a look at link structures consisting of a line of nodes or a complete graph where every node links to all others and different ways to combine the two. Both the ordinary normalized version of PageRank as well as a non-normalized version of PageRank found by solving corresponding linear system will be considered. We will see that it is possible to find explicit formulas for the PageRank in some simple link structures and using these formulas take a more in-depth look at the behavior of the ranking as the system changes.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:49:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500});

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- sv-SE
- Other locale

Output formathtml text asciidoc rtf $(function(){PrimeFaces.cw("SelectOneMenu","widget_formSmash_lower_j_idt965",{id:"formSmash:lower:j_idt965",widgetVar:"widget_formSmash_lower_j_idt965"});});

- html
- text
- asciidoc
- rtf