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BETA
Silvestrov, Sergei, ProfessorORCID iD iconorcid.org/0000-0003-4554-6528
Alternative names
Publications (10 of 154) Show all publications
Betuel, C., Malyarenko, A., Ni, Y., Rancic, M. & Silvestrov, S. (2018). Calibration of Multiscale Two-Factor Stochastic Volatility Models: A Second-Order Asymptotic Expansion Approach. In: Christos H Skiadas (Ed.), : . Paper presented at SMTDA2018 5th Stochastic Modeling Techniques and Data Analysis International Conference - SMTDA 2018, Crete, Greece. ISAST: International Society for the Advancement of Science and Technology
Open this publication in new window or tab >>Calibration of Multiscale Two-Factor Stochastic Volatility Models: A Second-Order Asymptotic Expansion Approach
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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]

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.

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
Available from: 2018-09-30 Created: 2018-09-30 Last updated: 2018-10-01Bibliographically approved
Silvestrov, S., Hössjer, O., Malyarenko, A. & Mishura, Y. (2018). Dmitrii S. Silvestrov. In: Sergei Silvestrov Anatoliy Malyarenko Milica Rančić (Ed.), Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017. Paper presented at 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 (pp. 1-4). Paper presented at 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. Springer, 271
Open this publication in new window or tab >>Dmitrii S. Silvestrov
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]

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

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
Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2018-12-31Bibliographically approved
Javor, V., Lundengård, K., Rancic, M. & Silvestrov, S. (2018). Electrostatic discharge currents and their derivatives' approximation by piecewise power-exponential functions. Turkish Journal of Electrical Engineering and Computer Sciences, 26(2), 1093-1102
Open this publication in new window or tab >>Electrostatic discharge currents and their derivatives' approximation by piecewise power-exponential functions
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]

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 C1L . 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.

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)
Available from: 2017-09-28 Created: 2017-09-28 Last updated: 2018-12-17Bibliographically approved
Bäck, P., Richter, J. & Silvestrov, S. (2018). Hom-associative Ore extensions. Paper presented at 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. Journal of Physics, Conference Series, 965(1), Article ID 012006.
Open this publication in new window or tab >>Hom-associative Ore extensions
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]

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.

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
Available from: 2018-03-15 Created: 2018-03-15 Last updated: 2018-10-18Bibliographically approved
Bäck, P., Richter, J. & Silvestrov, S. (2018). Hom-associative Ore extensions and weak unitalizations. International Electronic Journal of Algebra, 24, 174-194
Open this publication in new window or tab >>Hom-associative Ore extensions and weak unitalizations
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]

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.

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)
Available from: 2018-07-05 Created: 2018-07-05 Last updated: 2018-08-16Bibliographically approved
Lundengård, K., Österberg, J. & Silvestrov, S. (2018). Optimization of the Determinant of the Vandermonde Matrix and Related Matrices. Methodology and Computing in Applied Probability, 20(4), 1417-1428
Open this publication in new window or tab >>Optimization of the Determinant of the Vandermonde Matrix and Related Matrices
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]

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.

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)
Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2019-01-04Bibliographically approved
Tumwesigye, A. B., Richter, J. & Silvestrov, S. (2018). Ore extensions of function algebras. In: : . Paper presented at International Conference "Stochastic Processes and Algebraic Structures" (SPAS2017).
Open this publication in new window or tab >>Ore extensions of function algebras
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)
Available from: 2018-04-13 Created: 2018-04-13 Last updated: 2018-12-31Bibliographically approved
Engström, C. & Silvestrov, S. (2018). PageRank for networks, graphs and Markov chains. Theory of Probability and Mathematical Statistics, 96, 59-82
Open this publication in new window or tab >>PageRank for networks, graphs and Markov chains
2018 (English)In: Theory of Probability and Mathematical Statistics, ISSN 0868-6904, Vol. 96, p. 59-82Article in journal (Refereed) Published
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.

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)
Available from: 2017-09-30 Created: 2017-09-30 Last updated: 2019-01-04Bibliographically approved
Abola, B., Biganda, P., Engström, C., Mango, J. M., Kakuba, G. & Silvestrov, S. (2018). PageRank in evolving tree graphs. In: Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić (Ed.), Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017. Paper presented at 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 (pp. 375-390). Paper presented at 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. Springer, 271
Open this publication in new window or tab >>PageRank in evolving tree graphs
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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]

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.

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
Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2018-12-31Bibliographically approved
Silvestrov, S., Malyarenko, A. & Rančić, M. (2018). Preface. In: Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić (Ed.), Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 (pp. vii-x). Springer, 271
Open this publication in new window or tab >>Preface
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)
Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2019-01-15Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-4554-6528