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Malyarenko, AnatoliyORCID iD iconorcid.org/0000-0002-0139-0747
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Publications (10 of 99) Show all publications
Malyarenko, A., Mishura, Y., Ralchenko, K. & Shklyar, S. (2023). Entropy and alternative entropy functionals of fractional Gaussian noise as the functions of Hurst index. Fractional Calculus and Applied Analysis
Open this publication in new window or tab >>Entropy and alternative entropy functionals of fractional Gaussian noise as the functions of Hurst index
2023 (English)In: Fractional Calculus and Applied Analysis, ISSN 1311-0454, E-ISSN 1314-2224Article in journal (Refereed) Published
Abstract [en]

This paper is devoted to the study of the properties of entropy as a function of the Hurst index, which corresponds to the fractional Gaussian noise. Since the entropy of the Gaussian vector depends on the determinant of the covariance matrix, and the behavior of this determinant as a function of the Hurst index is rather difficult to study analytically at high dimensions, we also consider simple alternative entropy functionals, whose behavior, on the one hand, mimics the behavior of entropy and, on the other hand, is not difficult to study. Asymptotic behavior of the normalized entropy (so called entropy rate) is also studied for the entropy and for the alternative functionals.

Keywords
Fractional Gaussian noise, Hurst index, Entropy, Entropy functionals, Entropy rate
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-62415 (URN)10.1007/s13540-023-00155-2 (DOI)000980824200002 ()2-s2.0-85156247682 (Scopus ID)
Funder
Swedish Foundation for Strategic Research, UKR22-0017The Research Council of Norway, 274410The Research Council of Norway, 274410
Available from: 2023-05-08 Created: 2023-05-08 Last updated: 2024-01-09Bibliographically approved
Malyarenko, A., Mishura, Y., Ralchenko, K. & Rudyk, Y. A. (2023). Properties of Various Entropies of Gaussian Distribution and Comparison of Entropies of Fractional Processes. Axioms, 12(11), Article ID 1026.
Open this publication in new window or tab >>Properties of Various Entropies of Gaussian Distribution and Comparison of Entropies of Fractional Processes
2023 (English)In: Axioms, ISSN 2075-1680, Vol. 12, no 11, article id 1026Article in journal (Refereed) Published
Abstract [en]

We consider five types of entropies for Gaussian distribution: Shannon, Rényi, generalized Rényi, Tsallis and Sharma–Mittal entropy, establishing their interrelations and their properties as the functions of parameters. Then, we consider fractional Gaussian processes, namely fractional, subfractional, bifractional, multifractional and tempered fractional Brownian motions, and compare the entropies of one-dimensional distributions of these processes.

Place, publisher, year, edition, pages
Basel: MDPI, 2023
Keywords
Shannon entropy; Rényi entropy; Tsallis entropy; Sharma–Mittal entropy; normal distribution; fractional Brownian motion; subfractional Brownian motion; bifractional Brownian motion; multifractional Brownian motion; tempered fractional Brownian motion
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-64641 (URN)10.3390/axioms12111026 (DOI)001120792100001 ()
Funder
Swedish Foundation for Strategic Research, UKR22-0017The Research Council of Norway, 274410
Available from: 2023-10-31 Created: 2023-10-31 Last updated: 2024-01-03Bibliographically approved
Malyarenko, A. & Ostoja-Starzewski, M. (2023). Tensor- and spinor-valued random fields with applications to continuum physics and cosmology. Probability Surveys, 20(none), 1-86
Open this publication in new window or tab >>Tensor- and spinor-valued random fields with applications to continuum physics and cosmology
2023 (English)In: Probability Surveys, E-ISSN 1549-5787, Vol. 20, no none, p. 1-86Article in journal (Refereed) Published
Abstract [en]

In this paper, we review the history, current state-of-art, and physical applications of the spectral theory of two classes of random functions. One class consists of homogeneous and isotropic random fields defined on a Euclidean space and taking values in a real finite-dimensional linear space. In applications to continuum physics, such a field describes the physical properties of a homogeneous and isotropic continuous medium in the situation, when a microstructure is attached to all medium points.The range of the field is the fixed point set of a symmetry class, where two compact Lie groups act by orthogonal representations. The material symmetry group of a homogeneous medium is the same at each point and acts trivially, while the group of physical symmetries may act nontrivially. In an isotropic random medium, the rank 1 (resp., rank 2) correlation tensors of the field transform under the action of the group of physical symmetries according to the above representation (resp., its tensor square), making the field isotropic. Another class consists of isotropic random cross-sections of homogeneous vector bundles over a coset space of a compact Lie group. In applications to cosmology, the coset space models the sky sphere, while the random crosssection models a cosmic background. The Cosmological Principle ensures that the cross-section is isotropic.For the convenience of the reader, a necessary material from multilinear algebra, representation theory, and differential geometry is reviewed in Appendix.

Place, publisher, year, edition, pages
The Hague, The Netherlands: , 2023
Keywords
Random field, cosmic microwave background, microstructure, spectral expansion
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-61434 (URN)10.1214/22-ps12 (DOI)000975036600001 ()
Available from: 2023-01-05 Created: 2023-01-05 Last updated: 2023-07-19Bibliographically approved
Muhumuza, A. K., Lundengård, K., Malyarenko, A., Silvestrov, S., Mango, J. M. & Kakuba, G. (2023). The Wishart Distribution on Symmetric Cones. In: Sergei Silvestrov, Anatoliy Malyarenko (Ed.), Non-commutative and Non-associative Algebra and Analysis Structures: SPAS 2019, Västerås, Sweden, September 30 - October 2. Paper presented at International Conference on Stochastic Processes and Algebraic Structures—From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October 2019 (pp. 661-684). Springer
Open this publication in new window or tab >>The Wishart Distribution on Symmetric Cones
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2023 (English)In: Non-commutative and Non-associative Algebra and Analysis Structures: SPAS 2019, Västerås, Sweden, September 30 - October 2 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Springer , 2023, p. 661-684Conference paper, Published paper (Refereed)
Abstract [en]

In this paper we discuss the extension of the Wishart probability distributions in higher dimension based on the boundary points of the symmetric cones in Jordan algebras. The symmetric cones form a basis for the construction of the degenerate and non-degenerate Wishart distributions in the field of Herm(m,C), Herm(m,H), Herm(3,O) that denotes respectively the Jordan algebra of all Hermitian matrices of size m× m with complex entries, the skew field H of quaternions, and the algebra O of octonions. This density is characterised by the Vandermonde determinant structure and the exponential weight that is dependent on the trace of the given matrix.

Place, publisher, year, edition, pages
Springer, 2023
Series
Springer Proceedings in Mathematics and Statistics, ISSN 21941009 ; 426
Keywords
Vandermonde determinant, Jordan algebra, Symmetric cone, Wishart distribution
National Category
Probability Theory and Statistics Algebra and Logic Mathematical Analysis
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-64593 (URN)10.1007/978-3-031-32009-5_23 (DOI)2-s2.0-85174443553 (Scopus ID)9783031320088 (ISBN)
Conference
International Conference on Stochastic Processes and Algebraic Structures—From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October 2019
Available from: 2023-10-30 Created: 2023-10-30 Last updated: 2023-12-27Bibliographically approved
Faouzi, T., Kondrashuk, I., Porcu, E. & Malyarenko, A. (2022). A deep look into the Dagum family of isotropic covariance functions. Journal of Applied Probability, 59(4), 1026-1041
Open this publication in new window or tab >>A deep look into the Dagum family of isotropic covariance functions
2022 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 59, no 4, p. 1026-1041Article in journal (Refereed) Published
Abstract [en]

The Dagum family of isotropic covariance functions has two parameters that allow fordecoupling of the fractal dimension and the Hurst effect for Gaussian random fields thatare stationary and isotropic over Euclidean spaces. Sufficient conditions that allow forpositive definiteness in $R^d$ of the Dagum family have been proposed on the basis ofthe fact that the Dagum family allows for complete monotonicity under some parameter restrictions. The spectral properties of the Dagum family have been inspected to a verylimited extent only, and this paper gives insight into this direction. Specifically, we studyfinite and asymptotic properties of the isotropic spectral density (intended as the Hankeltransform) of the Dagum model. Also, we establish some closed-form expressions forthe Dagum spectral density in terms of the Fox–Wright functions. Finally, we provideasymptotic properties for such a class of spectral densities.

Place, publisher, year, edition, pages
Cambridge: Cambridge University Press, 2022
Keywords
Hankel transforms, Mellin–Barnes transforms, spectral theory, positive-definite
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-59770 (URN)10.1017/jpr.2021.103 (DOI)000841660300001 ()2-s2.0-85142135252 (Scopus ID)
Available from: 2022-08-22 Created: 2022-08-22 Last updated: 2023-04-12Bibliographically approved
Albuhayri, M., Engström, C., Malyarenko, A., Ni, Y. & Silvestrov, S. (2022). An Improved Asymptotics of Implied Volatility in the Gatheral Model. In: Anatoliy Malyarenko, Ying Ni, Milica Rančić, Sergei Silvestrov (Ed.), Springer Proceedings in Mathematics and Statistics: . Paper presented at SPAS 2019, Västerås, Sweden, September 30–October 2 (pp. 3-13). Springer Nature, 408
Open this publication in new window or tab >>An Improved Asymptotics of Implied Volatility in the Gatheral Model
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2022 (English)In: Springer Proceedings in Mathematics and Statistics, Springer Nature, 2022, Vol. 408, p. 3-13Conference paper, Published paper (Refereed)
Abstract [en]

We study the double-mean-reverting model by Gatheral. Our previous results concerning the asymptotic expansion of the implied volatility of a European call option, are improved up to order 3, that is, the error of the approximation is ultimately smaller that the 1.5th power of time to maturity plus the cube of the absolute value of the difference between the logarithmic security price and the logarithmic strike price.

Place, publisher, year, edition, pages
Springer Nature, 2022
Series
Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009, E-ISSN 2194-1017 ; 408
Keywords
Double-mean-reverting model, Implied volatility
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-61400 (URN)10.1007/978-3-031-17820-7_1 (DOI)2-s2.0-85171525140 (Scopus ID)978-3-031-17819-1 (ISBN)978-3-031-17820-7 (ISBN)
Conference
SPAS 2019, Västerås, Sweden, September 30–October 2
Available from: 2022-12-31 Created: 2022-12-31 Last updated: 2023-10-04Bibliographically approved
Muhumuza, A. K., Lundengård, K., Malyarenko, A., Silvestrov, S., Mango, J. M. & Kakuba, G. (2022). Connections between the extreme points for Vandermonde determinants and minimizing risk measure in financial mathematics. In: Anatoliy Malyarenko, Ying Ni, Milica Rančić, Sergei Silvestrov (Ed.), Springer Proceedings in Mathematics and Statistics: . Paper presented at SPAS 2019, Västerås, Sweden, September 30–October 2 (pp. 587-623). Springer Nature
Open this publication in new window or tab >>Connections between the extreme points for Vandermonde determinants and minimizing risk measure in financial mathematics
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2022 (English)In: Springer Proceedings in Mathematics and Statistics, Springer Nature, 2022, p. 587-623Conference paper, Published paper (Refereed)
Abstract [en]

The extreme points of Vandermonde determinants when optimized on surfaces like spheres and cubes have various applications in random matrix theory, electrostatics and financial mathematics. In this study, we apply the extreme points of Vandermonde determinant when optimized on various surfaces to risk minimization in financial mathematics. We illustrate this by constructing the efficient frontiers represented by spheres, cubes and other general surfaces as applies to portfolio theory. The extreme points of Vandermonde determinant lying on such surfaces as efficient frontier would be used to determine the set of assets with minimum risk and maximum returns. This technique can also applied in optimal portfolio selection and asset pricing.

Place, publisher, year, edition, pages
Springer Nature, 2022
Keywords
Asset pricing, Optimal portfolio selection, Risk minimization, Vandermonde determinant
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-61409 (URN)978-3-031-17819-1 (ISBN)
Conference
SPAS 2019, Västerås, Sweden, September 30–October 2
Funder
Sida - Swedish International Development Cooperation Agency
Available from: 2023-01-01 Created: 2023-01-01 Last updated: 2023-10-04Bibliographically approved
Nohrouzian, H., Malyarenko, A. & Ni, Y. (2022). Constructing Trinomial Models Based on Cubature Method on Wiener Space: Applications to Pricing Financial Derivatives. In: : . Paper presented at 7th Stochastic Modeling Techniques and Data Analysis International Conference and Demographics 2022 Workshop.
Open this publication in new window or tab >>Constructing Trinomial Models Based on Cubature Method on Wiener Space: Applications to Pricing Financial Derivatives
2022 (English)Conference paper, Oral presentation with published abstract (Other academic)
Abstract [en]

This contribution deals with an extension to our developed novel cubature methods of degrees 5 on Wiener space. In our previous studies, we studied cubature formulae that are exact for all multiple Stratonovich integrals up to dimension equal to the degree. In fact, cubature method reduces solving a stochastic differential equation to solving a finite set of ordinary differential equations. Now, we apply the above methods to construct trinomial models and to price different financial derivatives. We will compare our numerical solutions with the Black’s and Black-Scholes models’ analytical solutions. The constructed model has practical usage in pricing American options and American-style derivatives.

Keywords
Cubature method, Stratonovich integral, Wiener space, stochastic market model
National Category
Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-59718 (URN)
Conference
7th Stochastic Modeling Techniques and Data Analysis International Conference and Demographics 2022 Workshop
Available from: 2022-08-08 Created: 2022-08-08 Last updated: 2022-08-15Bibliographically approved
Malyarenko, A., Mishura, Y., Olenko, A. & Ostoja-Starzewski, M. (2022). EDITORIAL. THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS, 106, 1-1
Open this publication in new window or tab >>EDITORIAL
2022 (English)In: THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS, ISSN 0094-9000, Vol. 106, p. 1-1Article in journal, Editorial material (Refereed) Published
Place, publisher, year, edition, pages
TARAS SHEVCHENKO NATL UNIV KYIV, FAC MECH & MATH, 2022
National Category
Mathematics
Identifiers
urn:nbn:se:mdh:diva-60670 (URN)10.1090/tpms/11722022 (DOI)000804247700001 ()
Available from: 2022-11-21 Created: 2022-11-21 Last updated: 2023-02-08Bibliographically approved
Malyarenko, A., Mishura, Y., Olenko, A. & Ostoja-starzewski, M. (2022). EDITORIAL. THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS, 106, 1-1
Open this publication in new window or tab >>EDITORIAL
2022 (English)In: THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS, ISSN 0094-9000, Vol. 106, p. 1-1Article in journal, Editorial material (Other academic) Published
Place, publisher, year, edition, pages
TARAS SHEVCHENKO NATL UNIV KYIV, FAC MECH & MATH, 2022
National Category
Mathematics
Identifiers
urn:nbn:se:mdh:diva-65168 (URN)10.1090/tpms/1172 (DOI)000809405400001 ()2-s2.0-85131427374 (Scopus ID)
Available from: 2023-12-21 Created: 2023-12-21 Last updated: 2023-12-21Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-0139-0747

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