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Silvestrov, Sergei, Professororcid.org/0000-0003-4554-6528

Open this publication in new window or tab >>Calibration of Multiscale Two-Factor Stochastic Volatility Models: A Second-Order Asymptotic Expansion Approach### Betuel, Canhanga

### Malyarenko, Anatoliy

### Ni, Ying

### Rancic, Milica

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); ### Silvestrov, Sergei

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_0_j_idt188_j_idt202",{id:"formSmash:j_idt184:0:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2018 (English)In: / [ed] Christos H Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2018Conference paper, Oral presentation with published abstract (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

ISAST: International Society for the Advancement of Science and Technology, 2018
##### Keywords

Option pricing model, asymptotic expansion of option price, stochastic volatility model, multiscale stochastic volatility, calibration
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-41091 (URN)978-618-5180-27-0 (ISBN)978-618-5180-29-4 (ISBN)
##### Conference

SMTDA2018 5th Stochastic Modeling Techniques and Data Analysis International Conference - SMTDA 2018, Crete, Greece
#####

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Available from: 2018-09-30 Created: 2018-09-30 Last updated: 2018-10-01Bibliographically approved

Faculty of Sciences, Dept of Mathematics and Computer Sciences, Eduardo Mondlane University, Mozambique.

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.

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.

Open this publication in new window or tab >>Dmitrii S. Silvestrov### Silvestrov, Sergei

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Hössjer, O.

### Malyarenko, Anatoliy

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Mishura, Y.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: 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. 1-4Chapter in book (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer, 2018
##### Series

Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009 ; 271
##### Keywords

Kiev University, Luleå Technical University, Mälardalen University, Stockholm University, Umeå University, Random processes, Technical universities, Stochastic systems
##### National Category

Mathematics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-41832 (URN)10.1007/978-3-030-02825-1_1 (DOI)2-s2.0-85058563975 (Scopus ID)978-3-030-02824-4 (ISBN)
##### Conference

International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications”, SPAS 2017; Västerås and Stockholm; Sweden; 4 October 2017 through 6 October 2017; Code 221789
#####

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Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2018-12-31Bibliographically approved

Department of Mathematics, Stockholm University, Sweden.

Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Ukraine.

This chapter presents short biographical notes about Professor Dmitri S. Silvestrov.

Open this publication in new window or tab >>Electrostatic discharge currents and their derivatives' approximation by piecewise power-exponential functions### Javor, Vesna

### Lundengård, Karl

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Rancic, Milica

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Silvestrov, Sergei

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Turkish Journal of Electrical Engineering and Computer Sciences, ISSN 1300-0632, E-ISSN 1303-6203, Vol. 26, no 2, p. 1093-1102Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Electrostatic discharge currents, N-peaked analytically extended function, Marquardt least-squares method, power-exponential function
##### National Category

Computational Mathematics Other Electrical Engineering, Electronic Engineering, Information Engineering
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-36536 (URN)10.3906/elk-1707-95 (DOI)000428723200037 ()2-s2.0-85044990579 (Scopus ID)
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Available from: 2017-09-28 Created: 2017-09-28 Last updated: 2018-12-17Bibliographically approved

University of Nis, Faculty of Electronic Eng., Serbia.

An analytically extended function based on power-exponential functions is used in this paper for approxi- mation of electrostatic discharge (ESD) currents and their derivatives. The Marquardt least-squares method (MLSM) is applied for obtaining nonlinear function parameters. IEC 61000-4-2 Standard ESD current is approximated, as well as some measured ESD currents' wave shapes. Power-exponential terms are extended at the local maxima and minima of the represented wave shape, so that this approximation is done from peak to peak. ESD current derivative is approxi- mated using the same procedure in order to obtain the continuous second order derivative of the current, as all piecewise functions are of differentiability class C^{1}L . Currents and their derivatives are often measured in ESD experiments so that their analytical representation is needed for simulation of ESD phenomena, better definition of standard requirements, and computation of the transient fields and induced effects.

Open this publication in new window or tab >>Hom-associative Ore extensions### Bäck, Per

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Richter, Johan

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Silvestrov, Sergei

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, Vol. 965, no 1, article id 012006Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Institute of Physics Publishing, 2018
##### National Category

Mathematics Algebra and Logic
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-38849 (URN)10.1088/1742-6596/965/1/012006 (DOI)000446028000006 ()2-s2.0-85042922463 (Scopus ID)
##### Conference

25th International Conference on Integrable Systems and Quantum Symmetries, ISQS 2017; Czech Technical UniversityPrague; Czech Republic; 6 June 2017 through 10 June 2017; Code 134824
#####

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Available from: 2018-03-15 Created: 2018-03-15 Last updated: 2018-10-18Bibliographically approved

We introduce hom-associative Ore extensions as non-associative, non-unital Ore extensions with a hom-associative multiplication, as well as give some necessary and sufficient conditions when such exist. Within this framework, we also construct a family of hom-associative Weyl algebras as generalizations of the classical analogue, and prove that they are simple.

Open this publication in new window or tab >>Hom-associative Ore extensions and weak unitalizations### Bäck, Per

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Richter, Johan

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Silvestrov, Sergei

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: International Electronic Journal of Algebra, ISSN 1306-6048, E-ISSN 1306-6048, Vol. 24, p. 174-194Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

hom-associative Ore extensions, hom-associative Weyl algebras, hom-associative algebras
##### National Category

Algebra and Logic
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-40202 (URN)10.24330/ieja.440245 (DOI)000438336600013 ()2-s2.0-85051115772 (Scopus ID)
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Available from: 2018-07-05 Created: 2018-07-05 Last updated: 2018-08-16Bibliographically approved

We introduce hom-associative Ore extensions as non-unital, nonassociative Ore extensions with a hom-associative multiplication, and give some necessary and sucient conditions when such exist. Within this framework, we construct families of hom-associative quantum planes, universal enveloping algebras of a Lie algebra, and Weyl algebras, all being hom-associative generalizations of their classical counterparts, as well as prove that the latter are simple. We also provide a way of embedding any multiplicative hom-associative algebra into a multiplicative, weakly unital hom-associative algebra, which we call a weak unitalization.

Open this publication in new window or tab >>Optimization of the Determinant of the Vandermonde Matrix and Related Matrices### Lundengård, Karl

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Österberg, Jonas

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Silvestrov, Sergei

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 20, no 4, p. 1417-1428Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

SPRINGER, 2018
##### Keywords

Vandermonde determinant, Optimization, Grobner basis, Orthogonal polynomials, Ellipsoid, Optimal experiment design, Homogeneous polynomials, 33C45, 11C20, 15B99, 08B99
##### National Category

Computational Mathematics Algebra and Logic
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-41818 (URN)10.1007/s11009-017-9595-y (DOI)000449431800019 ()2-s2.0-85033696033 (Scopus ID)
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Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2019-01-04Bibliographically approved

The value of the Vandermonde determinant is optimized over various surfaces, including the sphere, ellipsoid and torus. Lagrange multipliers are used to find a system of polynomial equations which give the local extreme points in its solutions. Using Grobner basis and other techniques the extreme points are given either explicitly or as roots of polynomials in one variable. The behavior of the Vandermonde determinant is also presented visually in some interesting cases.

Open this publication in new window or tab >>Ore extensions of function algebras### Tumwesigye, Alex Behakanira

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Richter, Johan

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Silvestrov, Sergei

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2018 (English)Conference paper, Oral presentation with published abstract (Other (popular science, discussion, etc.))
##### National Category

Algebra and Logic
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-38999 (URN)
##### Conference

International Conference "Stochastic Processes and Algebraic Structures" (SPAS2017)
#####

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Available from: 2018-04-13 Created: 2018-04-13 Last updated: 2018-12-31Bibliographically approved

Open this publication in new window or tab >>PageRank for networks, graphs and Markov chains### Engström, Christopher

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Silvestrov, Sergei

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Theory of Probability and Mathematical Statistics, ISSN 0868-6904, Vol. 96, p. 59-82Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

PageRank, random walk, Markov chain, graph, strongly connected component
##### National Category

Probability Theory and Statistics Computational Mathematics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-36589 (URN)10.1090/tpms/1034 (DOI)000412769200006 ()2-s2.0-85055703888 (Scopus ID)
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Available from: 2017-09-30 Created: 2017-09-30 Last updated: 2019-01-04Bibliographically approved

In this work it is described how a partitioning of a graph into components can be used to calculate PageRank in a large network and how such a partitioning can be used to re-calculate PageRank as the network changes. Although considered problem is that of calculating PageRank, it is worth to note that the same partitioning method could be used when working with Markov chains in general or solving linear systems as long as the method used for solving a single component is chosen appropriately. An algorithm for calculating PageRank using a modified partitioning of the graph into strongly connected components is described. Moreover, the paper focuses also on the calculation of PageRank in a changing graph from two different perspectives, by considering specific types of changes in the graph and calculating the difference in rank before and after certain types of edge additions or removals between components. Moreover, some common specific types of graphs for which it is possible to find analytic expressions for PageRank are considered, and in particular the complete bipartite graph and how PageRank can be calculated for such a graph. Finally, several open directions and problems are described.

Open this publication in new window or tab >>PageRank in evolving tree graphs### Abola, Benard

### Biganda, Pitos

### Engström, Christopher

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Mango, J. M.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); ### Kakuba, G.

### Silvestrov, Sergei

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_8_j_idt188_j_idt202",{id:"formSmash:j_idt184:8:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2018 (English)In: 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]

##### Place, publisher, year, edition, pages

Springer, 2018
##### Series

Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009 ; 271
##### Keywords

Breadth-first search, Forward edge, PageRank, Random walk, Tree, Forestry, Graph theory, Iterative methods, Random processes, Stochastic systems, Trees (mathematics)
##### National Category

Computational Mathematics Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-41833 (URN)10.1007/978-3-030-02825-1_16 (DOI)2-s2.0-85058567338 (Scopus ID)978-3-030-02824-4 (ISBN)
##### Conference

International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications”, SPAS 2017; Västerås and Stockholm; Sweden; 4 October 2017 through 6 October 2017; Code 221789
#####

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Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2018-12-31Bibliographically approved

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.

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.

Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.

Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.

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.

Open this publication in new window or tab >>Preface### Silvestrov, Sergei

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Malyarenko, Anatoliy

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Rančić, Milica

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: 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. vii-xChapter in book (Refereed)
##### Place, publisher, year, edition, pages

Springer, 2018
##### Series

Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-41831 (URN)2-s2.0-85058576948 (Scopus ID)978-3-030-02824-4 (ISBN)978-3-030-02825-1 (ISBN)
#####

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Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2019-01-15Bibliographically approved