mdh.sePublications
Change search
Link to record
Permanent link

Direct link
BETA
Malyarenko, AnatoliyORCID iD iconorcid.org/0000-0002-0139-0747
Alternative names
Publications (10 of 61) Show all publications
Karimi, P., Malyarenko, A., Ostoja-Starzewski, M. & Zhang, X. (2020). RVE problem: mathematical aspects and related stochastic mechanics. International Journal of Engineering Science, 146, Article ID 103169.
Open this publication in new window or tab >>RVE problem: mathematical aspects and related stochastic mechanics
2020 (English)In: International Journal of Engineering Science, ISSN 0020-7225, E-ISSN 1879-2197, Vol. 146, article id 103169Article in journal (Refereed) Published
Abstract [en]

The paper examines (i) formulation of field problems of mechanics accounting for a random material microstructure and (ii) solution of associated boundary value problems. The adopted approach involves upscaling of constitutive properties according to the Hill--Mandel condition, as the only method yielding hierarchies of scale-dependent bounds and their statistics for a wide range of (non)linear elastic and inelastic, coupled-field, and even electromagnetic problems requiring (a) weakly homogeneous random fields and (b) corresponding variational principles. The upscaling leads to statistically homogeneous and isotropic mesoscale tensor random fields (TRFs) of constitutive\ properties, whose realizations are, in general, everywhere anisotropic. A summary of most general admissible correlation tensors for TRFs of ranks 1, \dots, 4 is given. A method of solving boundary value problems based on the TRF input is discussed in terms of torsion of a randomly structured rod. Given that many random materials encountered in nature (e.g., in biological and geological structures) are fractal and possess long-range correlations, we also outline a method for simulating such materials, accompanied by an application to wave propagation.

Place, publisher, year, edition, pages
Elsevier, 2020
Keywords
multiscale problems, RVE, scale-dependent bounds, stochastic mechanics, tensor random fields
National Category
Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-45886 (URN)10.1016/j.ijengsci.2019.103169 (DOI)000502882800006 ()2-s2.0-85074748193 (Scopus ID)
Available from: 2019-11-01 Created: 2019-11-01 Last updated: 2020-02-19Bibliographically approved
Malyarenko, A. & Ostoja-Starzewski, M. (2020). Tensor Random Fields in Continuum Mechanics. In: Altenbach, Holm and Öchsner, Andreas (Ed.), Encyclopedia of Continuum Mechanics: (pp. 2433-2441). Berlin, Heidelberg: Springer Berlin/Heidelberg
Open this publication in new window or tab >>Tensor Random Fields in Continuum Mechanics
2020 (English)In: Encyclopedia of Continuum Mechanics / [ed] Altenbach, Holm and Öchsner, Andreas, Berlin, Heidelberg: Springer Berlin/Heidelberg, 2020, p. 2433-2441Chapter in book (Refereed)
Place, publisher, year, edition, pages
Berlin, Heidelberg: Springer Berlin/Heidelberg, 2020
Keywords
Conductivity; Elasticity; Random fields; Stochastics; Uncertainty quantification
National Category
Probability Theory and Statistics Other Physics Topics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-38883 (URN)10.1007/978-3-662-53605-6_71-1 (DOI)978-3-662-53605-6 (ISBN)
Available from: 2018-03-26 Created: 2018-03-26 Last updated: 2020-03-19Bibliographically approved
Ma, C. & Malyarenko, A. (2020). Time-Varying Isotropic Vector Random Fields on Compact Two-Point Homogeneous Spaces. Journal of theoretical probability, 33(1), 319-339
Open this publication in new window or tab >>Time-Varying Isotropic Vector Random Fields on Compact Two-Point Homogeneous Spaces
2020 (English)In: Journal of theoretical probability, ISSN 0894-9840, E-ISSN 1572-9230, Vol. 33, no 1, p. 319-339Article in journal (Refereed) Published
Abstract [en]

A general form of the covariance matrix function is derived in this paper for a vector random field that is isotropic and mean square continuous on a compact connected two-point homogeneous space and stationary on a temporal domain. A series representation is presented for such a vector random field which involves Jacobi polynomials and the distance defined on the compact two-point homogeneous space.

Keywords
Covariance matrix function Elliptically contoured random field Gaussian random field Isotropy Stationarity Jacobi polynomials
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-41692 (URN)10.1007/s10959-018-0872-7 (DOI)
Note

This article has been recommended in ResearchGate by Sigurdur Helgason

Available from: 2018-12-18 Created: 2018-12-18 Last updated: 2020-03-19Bibliographically approved
Malyarenko, A. & Ostoja-Starzewski, M. (2020). Towards stochastic continuum damage mechanics. International Journal of Solids and Structures, 184, 202-210
Open this publication in new window or tab >>Towards stochastic continuum damage mechanics
2020 (English)In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 184, p. 202-210Article in journal (Refereed) Published
Abstract [en]

In classical continuum damage mechanics, the distribution of cracks over differently oriented planes is an even deterministic function defined on the unit sphere. The coefficients of its Fourier expansion are completely symmetric and completely traceless tensors of even rank, the so-called fabric or damage tensors. We propose a stochastic generalisation of the above described mathematical model, where damage tensors are mean-square continuous wide-sense homogeneous and isotropic random fields.

Place, publisher, year, edition, pages
Elsevier, 2020
Keywords
Tensor random field, Damage mechanics, Damage tensor, Fabric tensor
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-45222 (URN)10.1016/j.ijsolstr.2019.02.023 (DOI)000509816700015 ()2-s2.0-85062960537 (Scopus ID)
Available from: 2019-09-16 Created: 2019-09-16 Last updated: 2020-02-20Bibliographically approved
Ni, Y., Nohrouzian, H. & Malyarenko, A. (2019). An Arbitrage-Free Large Market Model for Forward Spread Curves. In: Christos H. Skiadas (Ed.), Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019: . Paper presented at ASMDA2019, 18th Applied Stochastic Models and Data Analysis International Conference (pp. 593-605). ISAST: International Society for the Advancement of Science and Technology
Open this publication in new window or tab >>An Arbitrage-Free Large Market Model for Forward Spread Curves
2019 (English)In: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019 / [ed] Christos H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2019, p. 593-605Conference paper, Published paper (Refereed)
Abstract [en]

Before the financial crisis started in 2007,the forward rate agreement(FRA) contracts could be perfectly replicated by overnight indexed swap (OIS) zerocouponbonds. After the crisis, the simply compounded risk-free OIS forward rate became less than the FRA rate. Using the approach by Cuchiero et al. [9], we constructan arbitrage-free market model, where the forward spread curves for a given finitetenor structure are described as a mild solution to a boundary value problem (BVP)for a system of infinite-dimensional stochastic differential equations. The constructedfinancial market is large: it contains infinitely many OIS zero coupon bonds and FRAcontracts with all possible maturities. We also investigate the necessary assumptionsand conditions which guarantee existence, uniqueness and non-negativity of solutionsto the obtained BVP.

Place, publisher, year, edition, pages
ISAST: International Society for the Advancement of Science and Technology, 2019
Keywords
Forward Rate Agreement, Overnight Index Swap, Large Market, Mild Solution, Wiener Space, Fundamental Theorem of Asset Pricing for Large Market, Existence, Uniqueness, Non-Negativity
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-47132 (URN)978-618-5180-33-1 (ISBN)
Conference
ASMDA2019, 18th Applied Stochastic Models and Data Analysis International Conference
Available from: 2020-02-20 Created: 2020-02-20 Last updated: 2020-02-24Bibliographically approved
Murara, J.-P., Malyarenko, A., Rančić, M. & Silvestrov, S. (2019). Forecasting Stochastic Volatility for Exchange Rates using EWMA. In: Christos H. Skiadas (Ed.), Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019: . Paper presented at ASMDA2019, 18th Applied Stochastic Models and Data Analysis International Conference (pp. 583-591). ISAST: International Society for the Advancement of Science and Technology
Open this publication in new window or tab >>Forecasting Stochastic Volatility for Exchange Rates using EWMA
2019 (English)In: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019 / [ed] Christos H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2019, p. 583-591Conference paper, Published paper (Refereed)
Abstract [en]

In risk management, foreign investors or multinational corporations are highly interested in knowing how volatile acurrency is in order to hedge risk. In this paper, using daily exchange rates and the Exponential Weighted Moving Average (EWMA) model, we perform volatility forecasting. We will investigate how used available time series affect the forecastings, i.e. how reliable our forecasting is depending on the period of used available data. We will also experiment the effects of the decay factor appearing in the model used on the forecasts.The results show that for the data used, it is optimal to use a smaller value of the decay factor and also for longer out-of-sample periods the forecasts get closer to the reality.

Place, publisher, year, edition, pages
ISAST: International Society for the Advancement of Science and Technology, 2019
Keywords
Exchange rate, Stochastic Volatility, Forecasting, FX Option
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-47124 (URN)978-618-5180-33-1 (ISBN)
Conference
ASMDA2019, 18th Applied Stochastic Models and Data Analysis International Conference
Funder
Sida - Swedish International Development Cooperation Agency
Available from: 2020-02-20 Created: 2020-02-20 Last updated: 2020-02-24Bibliographically approved
Murara, J.-P., Canhanga, B., Malyarenko, A. & Silvestrov, S. (2019). Pricing European Options under two-dimensional Black-Scholes Equation by two different approaches. In: Christos H. Skiadas (Ed.), Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019: . Paper presented at ASMDA2019, 18th Applied Stochastic Models and Data Analysis International Conference (pp. 573-582). ISAST: International Society for the Advancement of Science and Technology
Open this publication in new window or tab >>Pricing European Options under two-dimensional Black-Scholes Equation by two different approaches
2019 (English)In: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019 / [ed] Christos H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2019, p. 573-582Conference paper, Published paper (Refereed)
Abstract [en]

In the option pricing process, Black-Scholes (1973) solved a partial differential equation and introduced a model to determine the price of an option. While dealing with many problems in financial engineering, the application of Partial Differential Equations (PDEs) is fundamental to explain the changes that occur in the evolved systems. In this paper, we consider the European call option pricing problem that involves a two-dimensional Black-Scholes PDE. We transform the final time condition presented in [7] and compare the numerical prices using Crank-Nicolson scheme with analytic approximation prices obtained for a European basket option. Conclusions related to different parameters effects are given based on obtained results.

Place, publisher, year, edition, pages
ISAST: International Society for the Advancement of Science and Technology, 2019
Keywords
Stochastic Volatility, 2D Black-Scholes PDE, Crank-Nicolson Method, Basket option, Compound exchange option
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-47088 (URN)978-618-5180-33-1 (ISBN)
Conference
ASMDA2019, 18th Applied Stochastic Models and Data Analysis International Conference
Funder
Sida - Swedish International Development Cooperation Agency
Available from: 2020-02-20 Created: 2020-02-20 Last updated: 2020-02-24Bibliographically approved
Malyarenko, A., Ni, Y., Canhanga, B. & Silvestrov, S. (2018). Advanced Monte Carlo pricing of European options in a market model with two stochastic volatilities. In: Christos H Skiadas (Ed.), Proceedings : 5th Stochastic Modeling Techniques and Data Analysis International Conference withDemographics Workshop (SMTDA2018): . Paper presented at 12 -15 June 2018, Cultural Centre of Chania, Crete, Greece (pp. 409-422). ISAST: International Society for the Advancement of Science and Technology
Open this publication in new window or tab >>Advanced Monte Carlo pricing of European options in a market model with two stochastic volatilities
2018 (English)In: Proceedings : 5th Stochastic Modeling Techniques and Data Analysis International Conference withDemographics Workshop (SMTDA2018) / [ed] Christos H Skiadas, ISAST: International Society for the Advancement of Science and Technology, 2018, p. 409-422Conference paper, Published paper (Refereed)
Abstract [en]

We consider a market model with four correlated factors and two stochastic volatilities, one of which is rapid-changing, while another one is slow-changing in time. An advanced Monte Carlo methods based on the theory of cubature in Wiener space, is used to find the no-arbitrage price of the European call option in the above model.

Place, publisher, year, edition, pages
ISAST: International Society for the Advancement of Science and Technology: , 2018
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-43299 (URN)
Conference
12 -15 June 2018, Cultural Centre of Chania, Crete, Greece
Available from: 2019-05-02 Created: 2019-05-02 Last updated: 2019-12-14Bibliographically approved
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
Show others...
2018 (English)In: / [ed] Christos H Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2018Conference paper, Oral presentation with published abstract (Refereed)
Abstract [en]

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
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-0139-0747

Search in DiVA

Show all publications