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  • 1.
    Abdumuminov, Shuhrat
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Esteky, David Emanuel
    Mälardalen University, School of Education, Culture and Communication.
    Black-Litterman Model: Practical Asset Allocation Model Beyond Traditional Mean-Variance2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    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.

  • 2.
    Andersson, Fredrik K.
    et al.
    WorldLight.com AB, Sweden.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication.
    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]

    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.

  • 3.
    Andrejs, Matveevs
    et al.
    Riga Technical University, Latvia.
    Fjodorovs, Jegors
    Riga Technical University, Latvia.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Algorithms of the Copula Fit to the Nonlinear Processes in the Utility Industry2017In: Procedia Computer Science, ISSN 1877-0509, E-ISSN 1877-0509, Vol. 104, p. 572-577Article in journal (Refereed)
    Abstract [en]

    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.

  • 4.
    Betuel, Canhanga
    et al.
    Faculty of Sciences, Dept of Mathematics and Computer Sciences, Eduardo Mondlane University, Mozambique.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ni, Ying
    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.
    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]

    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.

  • 5. Biffi, Elena
    et al.
    D'Amico, Guillermo
    Di Biase, G
    Janssen, J
    Manca, Raimondo
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication.
    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)
  • 6. Biffi, Elena
    et al.
    D'Amigo, Guillermo
    Di Biase, Giuseppe
    Janssen, Jacques
    Manca, Raimondo
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication.
    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)
  • 7.
    Bodnar, Olha
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Analysis of Key Comparisons with Two Reference Standards: Extended Random Effects Meta-AnalysisIn: Advanced Mathematical and Computational Tools in Metrology and Testing XI / [ed] Alistair B Forbes, Nien-Fan Zhang, Anna Chunovkina, Sascha Eichstädt, Singapore: World ScientificChapter in book (Refereed)
    Abstract [en]

    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.

  • 8.
    Bodnar, Olha
    et al.
    Physikalisch-Technische Bundesanstalt, Germany.
    Elster, Clemens
    Physikalisch-Technische Bundesanstalt, Germany.
    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]

    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.

  • 9.
    Bodnar, Olha
    et al.
    Physikalisch-Technische Bundesanstalt, Germany.
    Elster, Clemens
    Physikalisch-Technische Bundesanstalt, Germany.
    Wübbeler, Gerd
    Physikalisch-Technische Bundesanstalt, Germany.
    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]

    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

  • 10. Bodnar, Olha
    et al.
    Possolo, Antonio
    National Institute of Standards and Technology, USA.
    Approximate Bayesian evaluations of measurement uncertainty2018In: Metrologia, ISSN 0026-1394, E-ISSN 1681-7575, Vol. 55, p. 147-157Article in journal (Refereed)
    Abstract [en]

    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.

  • 11.
    Bodnar, Olha
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Possolo, Antonio
    National Institute of Standards and Technology, USA.
    Approximate Bayesian Evaluations of Measurement Uncertainty2018Conference paper (Other academic)
  • 12.
    Canhanga, Betuel
    et al.
    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.
    Murara, Jean-Paul
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ni, Ying
    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.
    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]

    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).

  • 13.
    Canhanga, Betuel
    et al.
    DMI, Eduardo Mondlane University, Maputo, Mozambique.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Murara, Jean-Paul
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ni, Ying
    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.
    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]

    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).

  • 14.
    Canhanga, Betuel
    et al.
    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.
    Murara, Jean-Paul
    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.
    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]

    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.

  • 15.
    Canhanga, Betuel
    et al.
    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.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ni, Ying
    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.
    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]

    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.

  • 16.
    Canhanga, Betuel
    et al.
    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.
    Ni, Ying
    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.
    Perturbation Methods for Pricing European Options in a Model with Two Stochastic Volatilities2015In: New Trends in Stochastic Modelling and Data Analysis / [ed] Raimondo Manca, Sally McClean, Christos H Skiadas, ISAST , 2015, p. 199-210Chapter in book (Refereed)
    Abstract [en]

    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.

  • 17.
    Canhanga, Betuel
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ni, Ying
    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.
    Malyarenko, Anatoliy
    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.
    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]

    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.

  • 18.
    Carkovs, Jevgenijs
    et al.
    Riga Technical University.
    Malyarenko, AnatoliyMälardalen University, School of Education, Culture and Communication.Pärna, KalevUniversity of Tartu.
    Exploring the world of financial engineering2011Collection (editor) (Other academic)
    Abstract [en]

    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.

  • 19.
    Drozdenko, Myroslav
    Mälardalen University, Department of Mathematics and Physics.
    Weak Convergence of First-Rare-Event Times for Semi-Markov Processes2007Doctoral thesis, monograph (Other scientific)
    Abstract [en]

    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 service

  • 20.
    Dupuch, Marie
    et al.
    CNRS UMR 8163 STL, Universit´e Lille 3, 59653 Villeneuve d’Ascq, France.
    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.
    Hamon, Thierry
    LIM&BIO UFR SMBH Universit´e Paris 13, France.
    Grabar, Natalia
    CNRS UMR 8163 STL, Universit´e Lille 3, 59653 Villeneuve d’Ascq, France.
    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]

    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.

  • 21.
    Ekheden, Erhard
    et al.
    Stockholm University.
    Silvestrov, Dmitrii
    Stockholm University.
    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]

    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.

  • 22.
    Engström, Christopher
    et al.
    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.
    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]

    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.

  • 23.
    Engström, Christopher
    et al.
    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.
    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]

    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.

  • 24.
    Engström, Christopher
    et al.
    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.
    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]

    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.

  • 25.
    Engström, Christopher
    et al.
    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.
    PageRank for networks, graphs and Markov chains2017In: Theory of Probability and Mathematical Statistics, ISSN 0868-6904, Vol. 96, p. 61-83Article in journal (Refereed)
    Abstract [en]

    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.

  • 26.
    Eriksson, Kimmo
    Mälardalen University, Department of Mathematics and Physics.
    Statistical and combinatorial aspects of comparative genomics2004In: Scandinavian Journal of Statistics, ISSN 0303-6898, Vol. 31, no 2, p. 203-216Article, review/survey (Refereed)
    Abstract [en]

    This document presents a survey of the statistical and combinatorial aspects of four areas of comparative genomics: gene order based measures of evolutionary distances between species, construction of phylogenetic trees, detection of horizontal transfer of genes, and detection of ancient whole genome duplications.

  • 27.
    Eriksson, Kimmo
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm Univ, Stockholm, Sweden.
    Cownden, Daniel
    Stockholm Univ, Stockholm, Sweden.
    Strimling, Pontus
    Stockholm Univ, Stockholm, Sweden.
    Social learning may lead to population level conformity without individual level frequency bias2017In: Scientific Reports, ISSN 2045-2322, E-ISSN 2045-2322, Vol. 7, article id 17341Article in journal (Refereed)
    Abstract [en]

    A requirement of culture, whether animal or human, is some degree of conformity of behavior within populations. Researchers of gene-culture coevolution have suggested that population level conformity may result from frequency-biased social learning: individuals sampling multiple role models and preferentially adopting the majority behavior in the sample. When learning from a single role model, frequency-bias is not possible. We show why a population-level trend, either conformist or anticonformist, may nonetheless be almost inevitable in a population of individuals that learn through social enhancement, that is, using observations of others' behavior to update their own probability of using a behavior in the future. The exact specification of individuals' updating rule determines the direction of the trend. These results offer a new interpretation of previous findings from simulations of social enhancement in combination with reinforcement learning, and demonstrate how results of dynamical models may strongly depend on seemingly innocuous choices of model specifications, and how important it is to obtain empirical data on which to base such choices.

  • 28.
    Eriksson, Kimmo
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University.
    Haggstrom, Olle
    Chalmers University of Technology, Sweden.
    Lord's Paradox in a Continuous Setting and a Regression Artifact in Numerical Cognition Research.2014In: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 9, no 4, p. e95949-e95949Article in journal (Refereed)
    Abstract [en]

    In this paper we review, and elaborate on, the literature on a regression artifact related to Lord's paradox in a continuous setting. Specifically, the question is whether a continuous property of individuals predicts improvement from training between a pretest and a posttest. If the pretest score is included as a covariate, regression to the mean will lead to biased results if two critical conditions are satisfied: (1) the property is correlated with pretest scores and (2) pretest scores include random errors. We discuss how these conditions apply to the analysis in a published experimental study, the authors of which concluded that linearity of children's estimations of numerical magnitudes predicts arithmetic learning from a training program. However, the two critical conditions were clearly met in that study. In a reanalysis we find that the bias in the method can fully account for the effect found in the original study. In other words, data are consistent with the null hypothesis that numerical magnitude estimations are unrelated to arithmetic learning.

  • 29.
    Ghimire, Sushil
    et al.
    Pulchowk Campus, Institute of Engineering, Tribhuvan University, Nepal.
    Gyan, Bahadur Thapa
    Pulchowk Campus, Institute of Engineering, Tribhuvan University, Nepal.
    Ghimire, Ram Prasad
    Department of Mathematical Sciences, School of Science, Kathmandu University, Nepal.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    A Survey on Queueing Systems with Mathematical Models and Applications2017In: American Journal of Operational Research, ISSN 2324-6537, E-ISSN 2324-6545, ISSN 2324-6537, Vol. 7, no 1, p. 1-14Article in journal (Refereed)
    Abstract [en]

    Queuing systems consist of one or more servers that provide some sort of services to arriving customers. Almost everyone has some experience of tedious time being in a queue during several daily life activities. It is reasonable to accept that service should be provided to the one who arrives first in the queue. But this rule always may not work. Sometimes the last comer or the customer in the high priority gets service earlier than the one who is waiting in the queue for a long time. All these characteristics are the interesting areas of research in the queueing theory. In this paper, we present some of the previous works of various researchers with brief explanations. We then carry out some of the mathematical expressions which represent the different queueing behaviors. In almost all the literatures, these queueing behaviors are examined with the help of mathematical simulations. Based on the previous contributions of researchers, our specific point of attraction is to study the finite capacity queueing models in which limited number of customers are served by a single or multiple number of servers and the batch queueing models where arrival or service or both occur in a bulk. Furthermore, we present some performance measure equations of some queueing models together with necessary components used in the queueing theory. Finally, we report some applications of queueing systems in supply chain management pointing out some areas of research as further works.

  • 30. Jonsson, Markus
    An exponential limit shape of random q-proportion Bulgarian solitaireManuscript (preprint) (Other academic)
    Abstract [en]

    We introduce -random -proportion Bulgarian solitaire (), played on n cards distributed in piles. In each pile, a number of cards equal to the proportion  of the pile size rounded upward to the closest integer are candidates to be picked. Each candidate card is picked with probability , independently of other candidate cards. This generalizes Popov's random Bulgarian solitaire, in which there is a single candidate card in each pile. Popov showed that a triangular limit shape is obtained for a fixed p as n tends to infinity. Here we let both  and  vary with n. We show that under the conditions  and  as , the -random -proportion Bulgarian solitaire has an exponential limit shape.

  • 31.
    Jonsson, Robin
    Mälardalen University, School of Education, Culture and Communication.
    Optimal Linear Combinations of Portfolios Subject to Estimation Risk2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The combination of two or more portfolio rules is theoretically convex in return-risk space, which provides for a new class of portfolio rules that gives purpose to the Mean-Variance framework out-of-sample. The author investigates the performance loss from estimation risk between the unconstrained Mean-Variance portfolio and the out-of-sample Global Minimum Variance portfolio. A new two-fund rule is developed in a specific class of combined rules, between the equally weighted portfolio and a mean-variance portfolio with the covariance matrix being estimated by linear shrinkage. The study shows that this rule performs well out-of-sample when covariance estimation error and bias are balanced. The rule is performing at least as good as its peer group in this class of combined rules.

  • 32.
    Jonsson, Robin
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Radeschnig, Jessica
    Mälardalen University, School of Education, Culture and Communication.
    Momentum Investment Strategies with Portfolio Optimization: A Study on Nasdaq OMX Stockholm Large Cap2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This report covers a study testing the possibility of adding portfolio optimization by mean-variance analysis as a tool to extend the concept of momentum strategies in contrast to naive allocation formed by Jegadeesh & Titman (1993). Further these active investment strategies are compared with a passive benchmark as well as a randomly selected portfolio over the entire study-period. The study showed that the naive allocation model outperformed the mean-variance model both economically as well as statistically. No indication where obtained for a lagged return effect when letting a mean-variance model choose weights for a quarterly holding period and the resulting investment recommendation is to follow a naive investment strategy within a momentum framework.

  • 33.
    Leonenko, Nikolai
    et al.
    Cardiff University, UK.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Matérn Class Tensor-Valued Random Fields and Beyond2017In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 168, p. 1276-1301Article in journal (Refereed)
    Abstract [en]

    We construct classes of homogeneous random fields on a three-dimensional Euclidean space that take values in linear spaces of tensors of a fixed rank and are isotropic with respect to a fixed orthogonal representation of the group of 3 × 3 orthogonal matrices.The constructed classes depend on finitely many isotropic spectral densities. We say that such a field belongs to either the Matérn or the dual Matérn class if all of the above densities are Matérn or dual Matérn. Several examples are considered.

  • 34.
    Li, Weitian
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Hong, Xi
    Mälardalen University, School of Education, Culture and Communication.
    Market illiquidity and market excess return: Cross-section and time-series effects: A study of the Shanghai stock exchange2013Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The purpose of the current paper is to explore the cross-sectional relationship between market illiquidity and market excess return on stocks traded in the Shanghai Stock Exchange(SSE)over-time; using data from monthly and yearly databases of CSMAR(China Securities Market and Accounting Research) and statistics annual Shanghai Stock Exchange from 2001.1-2012.12.

    We believe that the empirical tests on the stocks traded in the New York Stock Exchange (NYSE) of the well-established paper by Amihud(2002)would be potentially useful to be tested in a different setting, the SSE; in doing so, we apply the same illiquidity measure and estimating models to examine the hypotheses of the current study. In consideration of the aim of the current study, an illiquidity measure proposed by a Chinese scholar Huang (2009)is also applied in the empirical tests.

    Due to that Chinese stock market is still young and under development, any outcomes from the current study that are dissimilar to the ones appeared in Amihud(2002) in the sense of the effectiveness of market illiquidity have nothing to do with the utility of illiquidity theory; rather, different market characteristics should be taken into account, such as the unpredictability of frequent policy interventions on a Chinese stock market, following Wang Fang, Han Dong and Jiang Xianglin (2002).

  • 35.
    Lundengård, Karl
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Generalized Vandermonde matrices and determinants in electromagnetic compatibility2017Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    Matrices whose rows (or columns) consists of monomials of sequential powers are called Vandermonde matrices and can be used to describe several useful concepts and have properties that can be helpful for solving many kinds of problems. In this thesis we will discuss this matrix and some of its properties as well as a generalization of it and how it can be applied to curve fitting discharge current for the purpose of ensuring electromagnetic compatibility.

    In the first chapter the basic theory for later chapters is introduced. This includes the Vandermonde matrix and some of its properties, history, applications and generalizations, interpolation and regression problems, optimal experiment design and modelling of electrostatic discharge currents with the purpose to ensure electromagnetic compatibility.

    The second chapter focuses on finding the extreme points for the determinant for the Vandermonde matrix on various surfaces including spheres, ellipsoids, cylinders and tori. The extreme points are analysed in three dimensions or more.

    The third chapter discusses fitting a particular model called the p-peaked Analytically Extended Function (AEF) to data taken either from a standard for electromagnetic compatibility or experimental measurements. More specifically the AEF will be fitted to discharge currents from the IEC 62305-1 and IEC 61000-4-2 standards for lightning protection and electrostatic discharge immunity as well as some experimentally measured data of similar phenomena.

  • 36.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ogutu, Carolyne
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. University of Nairobi, Kenya.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ni, Ying
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Weke, P.
    University of Nairobi, Kenya.
    Construction of moment-matching multinomial lattices using Vandermonde matrices and Gröbner bases2017In: AIP Conference Proceedings / [ed] Sivasundaram, S, American Institute of Physics (AIP), 2017, Vol. 1798, p. 020094-1-020094-7, article id 020094Conference paper (Refereed)
    Abstract [en]

    In order to describe and analyze the quantitative behavior of stochastic processes, such as the process followed by a financial asset, various discretization methods are used. One such set of methods are lattice models where a time interval is divided into equal time steps and the rate of change for the process is restricted to a particular set of values in each time step. The well-known binomial- and trinomial models are the most commonly used in applications, although several kinds of higher order models have also been examined. Here we will examine various ways of designing higher order lattice schemes with different node placements in order to guarantee moment-matching with the process. 

  • 37.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ogutu, Carolyne
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. University of Nairobi, Nairobi, Kenya.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Weke, Patrick
    University of Nairobi, Nairobi, Kenya.
    Asian Options, Jump-Diffusion Processes on a Lattice, and Vandermonde Matrices2014In: Modern Problems in Insurance Mathematics / [ed] Silvestrov, Dmitrii, Martin-Löf, Anders, Springer International Publishing , 2014, p. 335-363Chapter in book (Refereed)
    Abstract [en]

    Asian options are options whose value depends on the average asset price during its lifetime. They are useful because they are less subject to price manipulations. We consider Asian option pricing on a lattice where the underlying asset follows the Merton–Bates jump-diffusion model. We describe the construction of the lattice using the moment matching technique which results in an equation system described by a Vandermonde matrix. Using some properties of Vandermonde matrices we calculate the jump probabilities of the resulting system. Some conditions on the possible jump sizes in the lattice are also given.

  • 38.
    Lundengård, Karl
    et al.
    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.
    Javor, Vesna
    University of Nis, Faculty of Electronic Eng., Serbia.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Novel Approach to Modelling of Lightning Current Derivative2017In: Facta Universitatis Series: Electronics and Energetics, ISSN 0353-3670, E-ISSN 2217-5997, Vol. 30, no 2, p. 245-256Article in journal (Refereed)
    Abstract [en]

    A new approach to mathematical modelling of lightning current derivative is proposed in this paper. It builds on the methodology, previously developed by the authors, for representing lightning currents and electrostatic discharge (ESD) currents waveshapes. It considers usage of a multi-peaked form of the analytically extended function (AEF) for approximation of current derivative waveshapes. The AEF function parameters are estimated using the Marquardt least-squares method (MLSM) and the framework for fitting the multi-peaked AEF to a waveshape with an arbitrary number of peaks is briefly described. This procedure is validated performing a few numerical experiments, including fitting the AEF to single- and multi-peaked waveshapes corresponding to measured current derivatives.

  • 39.
    Lundengård, Karl
    et al.
    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.
    Modelling mortality rates using the powerexponential function2017In: Booklet of abstracts of SPAS2017 - International Conference on Stochastic Processes and Algebraic Structures– From Theory Towards Applications, 2017Conference paper (Refereed)
    Abstract [en]

    There are many models for the mortality rates of humans and other organisms. A phenomenon that complicates the modelling of human mortality rates is a rapid increase in mortality rate for young adults (in western Europe this is especially pronounced at the age of 25). We will examine models for mortality rates based on power-exponential functions, compare them to empirical data for mortality rates and other models.

  • 40.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Strass, Belinda
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Boulougari, Andromachi
    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.
    Application of a Power-Exponential Function Based Model to Mortality Rates Forecasting2018In: Book of Abstracts 5th Stochastic Modeling Techniques and Data Analysis International Conference with Demographics Workshop - SMTDA2018 / [ed] Christos H Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2018Conference paper (Refereed)
    Abstract [en]

    Mortality rates of living organisms or equipment are modelled in different ways. Variation of mortality over a life span has different characteristics that put constraints and requirements on a model developed to represent it. A well-know problem that complicates modelling of human mortality rates is the "accident hump" occurring in early adulthood. The mortality rate model based on power-exponential functions, previously proposed by the authors, behaves as expected in that life period. Here, it will be compared to other models usually applied in practice and to empirical data. Models will be fitted to known data of measured death rates from many different countries using numerical techniques for curve-fitting with the non-linear least squares method. The properties of the model with respect to quality of fit and usefulness in applications such as insurance pricing or forecasting will be discussed.

  • 41.
    Lundgren, Robin
    Mälardalen University, Department of Mathematics and Physics.
    Optimal Stopping Domains for Discrete Time Knock Out American Options2007In: Recent Advances in Stochastic Modelling and Data Analysis: Chania, Greece, 29 May - 1 June 2007, World Scientific , 2007, p. 613-620Chapter in book (Refereed)
  • 42.
    Lundgren, Robin
    Mälardalen University, Department of Mathematics and Physics.
    Structure of Optimal Stopping Domains for American Options with Knock out Domains2007In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 13(29), no 4, p. 98-129Article in journal (Refereed)
    Abstract [en]

    American options give us the possibility to exercise them at any moment of time up to maturity. An optimal stopping domain for American type options is a domain that, if the underlying price process enters we should exercise the option. A knock out option is a American barrier option of knock out type, but with more general shape structure of the knock out domain. An algorithm for generating the optimal stopping domain for American type knock out options is constructed. Monte Carlo simulation is used to determine the structure of the optimal stopping domain. Results of the structural, and stability of studies are presented for different models of payoff functions and knock out domains.

  • 43.
    Lundgren, Robin
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication.
    Convergence and Approximation of Option Rewards for Multivariate Price Processes2009Report (Other (popular science, discussion, etc.))
    Abstract [en]

    Multivariate Markov price processes and American type options for such processes with generalpayoff functions with not more than polynomial rate of growth are considered. Convergence results are obtainedfor optimal reward functionals of American type options for perturbed multivariateMarkov processes and payoff functions. These results are applied to approximation tree type algorithmsfor American type options for exponential diffusion type priceprocesses including mean-reverse stochastic processesused to model stochastic dynamics of energy prices.

  • 44.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication.
    A family of series representations of the multiparameter fractional Brownian motion2011In: SEMINAR ON STOCHASTIC ANALYSIS, RANDOM FIELDS AND APPLICATIONS VI / [ed] Dalang, RC; Dozzi, M; Russo, F, Birkhäuser , 2011, p. 209-226Conference paper (Refereed)
    Abstract [en]

    We derive a family of series representations of the multiparameter fractional Brownian motion in the centred ball of radius R in the N-dimensional space R^N. Some known examples of series representations are shown to be the members of the family under consideration.

  • 45.
    Malyarenko, Anatoliy
    Mälardalen University, Department of Mathematics and Physics.
    A series expansion of a certain class of isotropic Gaussian random fields with homogeneous increments2004Report (Other academic)
  • 46.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication.
    An optimal series expansion of the multiparameter fractional Brownian motion2008In: Journal of theoretical probability, ISSN 0894-9840, E-ISSN 1572-9230, Vol. 21, no 2, p. 459-475Article in journal (Refereed)
    Abstract [en]

    We derive a series expansion for the multiparameter fractional Brownian motion. The derived expansion is proven to be rate optimal.

  • 47.
    Malyarenko, Anatoliy
    Mälardalen University, Department of Mathematics and Physics.
    Functional limit theorems for multiparameter fractional Brownian motion2004Report (Other academic)
    Abstract [en]

    We prove a general functional limit theorem for mul-tiparameter fractional Brownian motion. The functional law ofthe iterated logarithm, functional L ́evy’s modulus of continuityand many other results are its particular cases. Applications toapproximation theory are discussed.

  • 48.
    Malyarenko, Anatoliy
    Mälardalen University, Department of Mathematics and Physics.
    Functional limit theorems for multiparameter fractional Brownian motion2004In: Proceedings of the 6th World Congress of the Bernoulli Society for Mathematical Statistics and Probability, Barcelona, July 26--31 2004, 2004, p. 142-xxxConference paper (Refereed)
  • 49.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication.
    Functional limit theorems for multiparameter fractional Brownian motion2006In: Journal of theoretical probability, ISSN 0894-9840, E-ISSN 1572-9230, Vol. 19, no 2, p. 263-288Article in journal (Refereed)
    Abstract [en]

    We prove a general functional limit theorem for multiparameterfractional Brownian motion. The functional law of the iteratedlogarithm, functional Lévy's modulus of continuity and manyother results are its particular cases. Applications toapproximation theory are discussed.

  • 50.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication.
    Invariant random fields in vector bundles and application to cosmology2011In: Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, ISSN 0246-0203, Vol. 47, no 4, p. 1068-1095Article in journal (Refereed)
    Abstract [en]

    We develop the theory of invariant random fields in vector bundles. The spectral decomposition of an invariant random field in a homogeneous vector bundle generated by an induced representation of a compact connected Lie group G is btained. We discuss an application to the theory of relic radiation, where G = SO(3). A theorem about equivalence of two different groups of assumptions in cosmological theories is proved.

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