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  • 51.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication.
    Invariant random fields in vector bundles and application to cosmologyManuscript (preprint) (Other academic)
    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 obtained. We discuss an application to the theory of cosmic microwave background, where $G=SO(3)$. A theorem about equivalence of two different groups of assumptions in cosmological theories is proved.

  • 52.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Invariant random fields on spaces with a group action2013Book (Refereed)
    Abstract [en]

    The author describes the current state of the art in the theory of invariant random fields. This theory is based on several different areas of mathematics, including probability theory, differential geometry, harmonic analysis, and special functions. The present volume unifies many results scattered throughout the mathematical, physical, and engineering literature, as well as it introduces new results from this area first proved by the author. The book also presents many practical applications, in particular in such highly interesting areas as approximation theory, cosmology and earthquake engineering. It is intended for researchers and specialists working in the fields of stochastic processes, statistics, functional analysis, astronomy, and engineering. 

  • 53.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication.
    Lectures on cubature methods in financial engineering2011In: Exploring the world of financíal engineering / [ed] Jeegenijs Carkovs, Anatoliy Malyarenko, Kalev Pärna, Västerås: Mälardalen University , 2011, p. 48-65Chapter in book (Other academic)
    Abstract [en]

    We present a pedagogical introduction into cubature methods on Wiener space and their use in financial engineering. Some important parts of mathematics which are often omitted in study plans, are described in details. These includes the Riemann--Stiltjes integral, tensor products, and elements of Lie theory.

  • 54.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Spectral expansions of cosmological fields2015In: Journal of Statistical Science and Application, ISSN 2328-224X, Vol. 3, no 11-12, p. 175-193Article in journal (Refereed)
    Abstract [en]

    We give a review of the theory of random fields defined on the observable part of the Universe that satisfy the cosmological principle, i.e.,invariant with respect to the 6-dimensional group G of theisometries of the time slice of theFriedmann-Lemaitre-Robertson-Walker standard chart. Our new results include proof of spectral expansions of scalar and spin weighted G-invariant cosmological fields in open, flat, and closed cosmological models.

  • 55.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Spectral expansions of random sections of homogeneous vector bundles2017In: Teoriya Imovirnostei ta Matematychna Statystyka (THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS ), ISSN 0868-6904, Vol. 97, p. 142-156Article in journal (Refereed)
    Abstract [en]

    Tiny fluctuations of the Cosmic Microwave Background as well as various observable quantities obtained by spin raising and spin lowering of the effective gravitational lensing potential of distant galaxies and galaxy clusters, are described mathematically as isotropic random sections of homogeneousspin and tensor bundles. We consider the three existing approaches to rigourous constructing of the above objects, emphasising an approach based on the theory of induced group representations. Both orthogonal and unitary representations are treated in a unified manner. Several examples from astrophysics are included.

  • 56.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Spectral expansions of tensor-valued random fields2017In: AIP Conference Proceedings, Volume 1798, American Institute of Physics (AIP), 2017, Vol. 1798, p. 1-10, article id 020095Conference paper (Refereed)
    Abstract [en]

    In this paper, we review the theory of random fields that are defined on the space domain ℝ3, take values in a real finite-dimensional linear space V that consists of tensors of a fixed rank, and are homogeneous and isotropic with respect to an orthogonal representation of a closed subgroup G of the group O(3). A historical introduction, the statement of the problem, some current results, and a sketch of proofs are included.

  • 57.
    Malyarenko, Anatoliy
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Ma, Chunsheng
    Wichita State University.
    Time-Varying Isotropic Vector Random Fields on Compact Two-Point Homogeneous SpacesManuscript (preprint) (Other academic)
    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 acompact connected two-point homogeneous space and stationary on a temporal domain. A series representation is presented for such a vector random field, which involve Jacobi polynomials and the distance defined on the  compact two-point homogeneous space.

  • 58.
    Malyarenko, Anatoliy
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ostoja-Starzewski, Martin
    University of Illinois at Urbana-Champaign, US.
    A Random Field Formulation of Hooke’s Law in All Elasticity Classes2017In: Journal of elasticity, ISSN 0374-3535, E-ISSN 1573-2681, Vol. 127, no 2, p. 269-302Article in journal (Refereed)
    Abstract [en]

    For each of the 8 symmetry classes of elastic materials, we consider a homogeneousrandom field taking values in the fixed point set V of the corresponding class, that is isotropic with respect to the natural orthogonal representation of a group lying between the isotropy group of the class and its normaliser. We find the general form of the correlation tensors of orders 1 and 2 of such a field, and the field’s spectral expansion.

  • 59.
    Malyarenko, Anatoliy
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Ostoja-Starzewski, Martin
    University of Illinois at Urbana-Champaign, USA.
    A random field formulation of Hooke’s law in all elasticity classesManuscript (preprint) (Other academic)
    Abstract [en]

    For each of the 8 isotropy classes of elastic materials, we consider a homogeneous random field taking values in the fixed point set V of the corresponding class, that is isotropic with respect to the natural orthogonal representation of a group lying between the isotropy group of the class and its normaliser. We find the general form of the correlation tensors of orders 1 and 2 of such a field, and the field's spectral expansion.

  • 60.
    Malyarenko, Anatoliy
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ostoja-Starzewski, Martin
    University of Illinois at Urbana-Champaign, USA.
    Fractal planetary rings: energy inequalities and random field model2017In: International Journal of Modern Physics B, ISSN 0217-9792, Vol. 31, no 30, article id 1750236Article in journal (Refereed)
    Abstract [en]

    This study is motivated by a recent observation, based on photographs from the Cassini mission, that Saturn’s rings have a fractal structure in radial direction. Accordingly, two questions are considered: (1) What Newtonian mechanics argument in support of such a fractal structure of planetary rings is possible? (2) What kinematics model of such fractal rings can be formulated? Both challenges are based on taking planetary rings’ spatial structure as being statistically stationary in time and statistically isotropic in space, but statistically nonstationary in space. An answer to the first challenge is given through an energy analysis of circular rings having a self-generated, noninteger-dimensional mass distribution [V. E. Tarasov, Int. J. Mod Phys. B 19, 4103 (2005)]. The second issue is approached by taking the random field of angular velocity vector of a rotating particle of the ring as a random section of a special vector bundle. Using the theory of group representations, we prove that such a field is completely determined by a sequence of continuous positive-definite matrix-valued functions defined on the Cartesian square F^2 of the radial cross-section F, where F is a fat fractal.

  • 61.
    Malyarenko, Anatoliy
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ostoja-Starzewski, Martin
    University of Illinois at Urbana-Champaign, Champaign, United States .
    Spectral Expansion of Three-Dimensional Elasticity Tensor Random Fields2016In: Engineering Mathematics I: Electromagnetics, Fluid Mechanics, Material Physics and Financial Engineering / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016, p. 281-300Chapter in book (Refereed)
    Abstract [en]

    We consider a random field model of the 21-dimensional elasticity tensor. Representation theory is used to obtain the spectral expansion of the model in terms of stochastic integrals with respect to random measures.

  • 62.
    Malyarenko, Anatoliy
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ostoja-Starzewski, Martin
    University of Illinois at Urbana-Champaign.
    Spectral expansions of homogeneous and isotropic tensor-valued random fields2016In: Zeitschrift für angewandte Matematik und Physik ZAMP, ISSN 1420-9039, Vol. 67, no 3, article id 59Article in journal (Refereed)
    Abstract [en]

    We establish spectral expansions of tensor-valued homogeneous and isotropic random fields in terms of stochastic integrals with respect to orthogonal scattered random measures previously known only for the case of tensor rank 0. The fields under consideration take values in the 3-dimensional Euclidean space E3 and in the space S2(E3) of symmetric rank 2 tensors over E3. We find a link between the theory of random fields and the theory of finite-dimensional convex compact sets. These random fields furnish stepping-stone for models of rank 1 and rank 2 tensor-valued fields in continuum physics, such as displacement, velocity, stress, strain, providing appropriate conditions (such as the governing equation or positive-definiteness) are imposed.

  • 63.
    Malyarenko, Anatoliy
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ostoja-Starzewski, Martin
    University of Illinois at Urbana-Champaign.
    Statistically isotropic tensor random fields: correlation structures2014In: Mathematics and Mechanics of Complex Systems, ISSN 2325-3444, Vol. 2, no 2, p. 209-231Article in journal (Refereed)
    Abstract [en]

    Let V be a real finite-dimensional vector space. We introduce some physical problems that may be described by V-valued homogeneous and isotropic random fields on R 3 . We propose a general method for calculation of expectations and two-point correlation functions of such fields. Our results are equivalent to classical results by Robertson, when V = R 3 , and those by Lomakin, when V is the space of symmetric second-rank tensors over R 3 . Our solution involves an analogue of the classical Clebsch–Gordan coefficients.

  • 64.
    Malyarenko, Anatoliy
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ostoja-Starzewski, Martin
    University of Illinois at Urbana-Champaign.
    Tensor Random Fields in Continuum Mechanics2018In: Encyclopedia of Continuum Mechanics / [ed] Altenbach, Holm and Öchsner, Andreas, Berlin, Heidelberg: Springer Berlin/Heidelberg, 2018, p. 1-9Chapter in book (Refereed)
  • 65.
    Malyarenko, Anatoliy
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ostoja-Starzewski, Martin
    University of Illinois at Urbana-Champaign, USA.
    Tensor-Valued Random Fields in Continuum Physics2016In: Materials with internal structure: Multiscale and Multifield Modeling and Simulation / [ed] P. Trovalusci, Berlin/Heidelberg: Springer Science+Business Media B.V., 2016, p. 75-88Chapter in book (Refereed)
    Abstract [en]

    This article reports progress on homogeneous isotropic tensor random fields (TRFs) for continuum mechanics. The basic thrust is on determinin most general representations of the correlation functions as well as their spectral expansions. Once this is accomplished, the second step is finding the restrictionsdictated by a particular physical application. Thus, in the case of fields of material properties (like conductivity and stiffness), the restriction resides in the positive-definiteness, whereby a connection to experiments and/or computational micromechanics can be established. On the other hand, in the case of fields of dependent properties (e.g., stress, strain and displacement), restrictions are due to the respective field equations.

  • 66.
    Malyarenko, Anatoliy
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ostoja-Starzewski, Martin
    University of Illinois in Urbana-Champaign, USA.
    The spectral expansion of the elasticity random field2014In: AIP Conference Proceedings 1637 / [ed] S. Sivasundaram, 2014, p. 647-655Conference paper (Refereed)
    Abstract [en]

    We consider a deformable body that occupies a region D in the plane. In our model, the body's elasticity tensor H (x) is the restriction to D of a second-order mean-square continuous random field. Under translation, the expected value and the correlation tensor of the field H (x) do not change. Under action of an arbitrary element k of the orthogonal group O (2), they transform according to the reducible orthogonal representation k bar right arrow S-2 (S-2 (k)) of the above group. We find the spectral expansion of the correlation tensor R (x) of the elasticity field as well as the expansion of the field itself in terms of stochastic integrals with respect to a family of orthogonal scattered random measures.

  • 67.
    Malyarenko, Anatoliy
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Röman, Jan
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Swedbank, Sweden.
    Schyberg, Oskar
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Sensitivity Analysis of Catastrophe Bond Priceunder the Hull–White Interest Rate Model2016In: Engineering Mathematics I: Electromagnetics, Fluid Mechanics, Material Physics and Financial Engineering / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016Chapter in book (Refereed)
    Abstract [en]

    We consider a model, where the natural risk index is described by the Merton jump-diffusion while the risk-free interest rate is governed by the Hull–White stochastic differential equation. We price a catastrophe bond with payoff depending on finitely many values of the underlying index. The sensitivities of the bond price with respect to the initial condition, volatility of the diffusion component, and jump amplitude, are calculated using the Malliavin calculus approach.

  • 68.
    Malyarenko, Anatoliy
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Silvestrov, Dmitrii S.
    Mälardalen University, Department of Mathematics and Physics.
    Silvestrova, Evelina
    Mälardalen University, Department of Mathematics and Physics.
    Stochastic modelling of insurance business with dynamical control of investments2004In: 6th World Congress of Bernoulli Society for Mathematical Statistics and Probability, Barcelona, July 26--31 2004, 2004, p. page 181-Conference paper (Other academic)
  • 69.
    Mamchych, Tetyana
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Eastern European University, Lutsk, Ukraine.
    Wallin, Fredrik
    Mälardalen University, School of Business, Society and Engineering, Future Energy Center.
    Looking for Patterns in Residential Electricity Consumption2014In: Energy Procedia, ISSN 1876-6102, E-ISSN 1876-6102, Vol. 61, p. 1768-1771Article in journal (Refereed)
    Abstract [en]

    Residential electricity consumption is an important part of general energy use. Its detailed investigation, however, requires rich empirical data, here the data of Swedish households. The individual consumption is a time series of readings at certain time intervals (hourly, every ten minutes, or every minute, say). Series exhibit patterns, in terms of which they may be compared, and it is desirable to model similarity. Classical statistical methods (correlation, factor, and cluster analyses) are presently used for this purpose; they have the advantage of being more explicit than the techniques of adaptive data analysis that may recently have become excessively popular. The present work is methodological, preceding any massive statistical analyses. Factor analysis allowed describing individual styles in terms of time intervals (during a day) of maximal variability. Cluster analysis was used for finding groups of days with similar patterns; the obtained clusters can help interpreting the results of other methods. Comparing two households requires comparing two sets of time series; correlation analysis quantified the similarity between them.

  • 70.
    Manca, R.
    et al.
    Universit´a di Roma La Sapienza, Italy.
    Silvestrov, Dmitrii
    Mälardalen University, Department of Mathematics and Physics.
    Stenberg, Fredrik
    Mälardalen University, Department of Mathematics and Physics.
    Homogeneous backward semi-Markov reward models for insurance contracts2005In: Proceedings of ASMDA 2005 Conference: Brest, 2005, 2005, p. 959-967Conference paper (Other academic)
    Abstract [en]

    Numerical algorithms for eveluation of higher order moments for semi-Markov rewards processes are presented. Results of numerical experiments are given and commented.

  • 71.
    Mostafa Orand, Seyed
    et al.
    IslamicAzad University, Science and Research Branch, Saveh, Iran .
    Mirzazadeh, Abolfazl
    Kharazmi University, Tehran, Iran.
    Ahmadzadeh, Farzaneh
    Islamic Azad University, Karaj Branch, Iran.
    Talebloo, Farid
    Sufi Razi, Zanjan, Iran.
    Optimisation of the Inflationary Inventory Control Model under Stochastic Conditions with Simpson Approximation: Particle Swarm Optimisation Approach2015In: Iranian Journal of Management Studies, ISSN 2008-7055, Vol. 8, no 2, p. 203-220Article in journal (Refereed)
  • 72.
    Murara, Jean-Paul
    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.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Modelling electricity price series using regime-switching GARCH model2015In: 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. 713-725Conference paper (Refereed)
    Abstract [en]

    This paper implements and analyzes the Regime-Switching GARCH modelusing real NordPool Electricity spot data. We allow the model parameters to switch between a regular regime and a non-regular regime, which is justied by a so-called structural break behaviour of electricity price series. In splitting the two regimes we consider three criteria, namely the intercountry price difference criterion, the capacity/flow difference criterion and the spikes-in-Finland criterion. We study the correlation relationships among these criteria using the mean-square contingency coefficient and the co-occurrence measure. We also estimate our model parameters and present empirical validity of the model.

  • 73.
    Ni, Ying
    Mälardalen University, School of Education, Culture and Communication.
    Asymptotically Improper Perturbed Renewal Equations: Asymptotic Results and Their Applications2011Report (Other academic)
    Abstract [en]

    We consider a family of asymptotically improper perturbed renewal equations where the characteristics of the distribution functions generating the perturbed renewal equations are perturbed in a particular way. More specifically, those characteristics are nonlinear functions of the perturbation parameter such that they can be expanded into asymptotic expansions of a non-polynomial type with respect to the perturbation parameter. We give asymptotic results, namely the exponential asymptotic expansions, for the solutions of the perturbed renewal equations. An application to perturbed storage processes is also presented.

  • 74.
    Ni, Ying
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Exponential asymptotical expansions for ruin probability in a classical risk process with non-polynomial perturbations2014In: Modern Problems in Insurance Mathematics / [ed] Silvestrov, D., Martin-Löf, A. (eds), Springer, 2014, p. 69-94Chapter in book (Refereed)
    Abstract [en]

    In this paper we investigate the asymptotical behaviour of ruin probability in a classical compound Poisson risk process associated with perturbations in the claim size distributions and/or other parameters of the risk process. The novelty of this study is that we consider non-polynomial perturbations which include the polynomial perturbations as particular cases. The aim of the study is to develop exponential asymptotical expansions for the ruin probability as the initial capital goesto infinity and the perturbation parameter goes to zero, simultaneously but in a balanced manner. Numerical examples of risk processes with such type of perturbations are also given for illustrative purposes.

  • 75.
    Ni, Ying
    Mälardalen University, School of Education, Culture and Communication.
    NONLINEARLY PERTURBED RENEWAL EQUATIONS: THE NON-POLYNOMIAL CASE2012In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 84, p. 117-129Article in journal (Refereed)
    Abstract [en]

    Models of nonlinearly perturbed renewal equations with non-polynomial perturbations are studied. Exponential asymptotic expansions are given for the solutions to the perturbed renewal equations under consideration. An application to perturbed M/G/1/ queues is presented.

  • 76.
    Ni, Ying
    Mälardalen University, School of Education, Culture and Communication.
    Perturbed Renewal Equations with Non-Polynomial Perturbations2010Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis deals with a model of nonlinearly perturbed continuous-time renewal equation with nonpolynomial perturbations. The characteristics, namely the defect and moments, of the distribution function generating the renewal equation are assumed to have expansions with respect to a non-polynomial asymptotic scale: $\{\varphi_{\nn} (\varepsilon) =\varepsilon^{\nn \cdot \w}, \nn \in \mathbf{N}_0^k\}$  as $\varepsilon \to 0$, where $\mathbf{N}_0$ is the set of non-negative integers, $\mathbf{N}_0^k \equiv \mathbf{N}_0 \times \cdots \times \mathbf{N}_0, 1\leq k <\infty$ with the product being taken $k$ times and $\w$ is a $k$ dimensional parameter vector that satisfies certain properties. For the one-dimensional case, i.e., $k=1$, this model reduces to the model of nonlinearly perturbed renewal equation with polynomial perturbations which is well studied in the literature.  The goal of the present study is to obtain the exponential asymptotics for the solution to the perturbed renewal equation in the form of exponential asymptotic expansions and present possible applications.

    The thesis is based on three papers which study successively the model stated above. Paper A investigates the two-dimensional case, i.e. where $k=2$. The corresponding asymptotic exponential expansion for the solution to the perturbed renewal equation is given. The asymptotic results are applied to an example of the perturbed risk process, which leads to diffusion approximation type asymptotics for the ruin probability.  Numerical experimental studies on this example of perturbed risk process are conducted in paper B, where Monte Carlo simulation are used to study the accuracy and properties of the asymptotic formulas. Paper C presents the asymptotic results for the more general case where the dimension $k$ satisfies $1\leq k <\infty$, which are applied to the asymptotic analysis of the ruin probability in an example of perturbed risk processes with this general type of non-polynomial perturbations.  All the proofs of the theorems stated in paper C are collected in its supplement: paper D.

  • 77.
    Ni, Ying
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Canhanga, Betuel
    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.
    Approximation Methods of European Option Pricing in Multiscale Stochastic Volatility Model2017In: 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, American Institute of Physics (AIP), 2017, Vol. 1798, p. 020112-1-020112-10, article id 020112Conference paper (Refereed)
    Abstract [en]

    In the classical Black-Scholes model for financial option pricing, the asset price follows a geometric Brownian motion with constant volatility. Empirical findings such as volatility smile/skew, fat-tailed asset return distributions have suggested that the constant volatility assumption might not be realistic. A general stochastic volatility model, e.g. Heston model, GARCH model  and SABR volatility model , in which the variance/volatility itself follows typically a mean-reverting stochastic process, has shown to be superior in terms of capturing the empirical facts. However in order to capture more features of the volatility smile a two-factor, of double Heston type, stochastic volatility model is more useful as shown by Christoffersen, Heston and Jacobs.  We consider one specific type of such two-factor volatility models in which the volatility has multiscale mean-reversion rates. Our model contains two mean-reverting volatility processes with a fast and a slow reverting rate respectively. We consider the European option pricing problem under one type of the multiscale stochastic volatility model where the two volatility processes act as independent factors in the asset price process.  The novelty in this chapter is an approximating analytical solution using asymptotic expansion method which extends the authors earlier research in Canhanga et al. In addition we propose a numerical approximating solution using Monte-Carlo simulation. For completeness and for comparison we also implement the semi-analytical solution by Chiarella and Ziveyi using method of characteristics, Fourier and bivariate Laplace transforms.

  • 78.
    Ni, Ying
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Dmitrii
    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.
    Exponential asymptotics for nonlinearly perturbed renewal equation with non-polynomial perturbations2008In: Journal of Numerical and Applied Mathematics, ISSN 0868-6912, Vol. 96, no 1, p. 173-197Article in journal (Refereed)
    Abstract [en]

    The model of nonlinearly perturbedcontinuous-time renewal equation is studied in this paper.The perturbation conditions considered involve asymptoticalexpansions with respect to asymptotic scale$\{\varphi_{n,m}(\varepsilon) = \varepsilon^{n +m\omega}\}$,with $n, m$ being non-negative integers and $\omega >1$ beingirrational number. Such asymptotical scale results in non-polynomialtype of asymptotic expansions for solutions for perturbed renewalequations. An example of risk processes with perturbations describedabove and asymptotic expansions in diffusion approximation for ruinprobabilities in this model are given.

  • 79.
    Ogutu, Carolyne
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Lundengård, Karl
    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.
    Weke, Patrick
    University of Nairobi, Kenya.
    Pricing Asian Options using Moment Matching on a Multinomial Lattice2014In: 10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014 Conference date: 15–18 July 2014 Location: Narvik, Norway ISBN: 978-0-7354-1276-7 Editor: Seenith Sivasundaram Volume number: 1637 Published: 10 december 2014 / [ed] Seenith Sivasundaram, 2014, p. 759-765Conference paper (Refereed)
    Abstract [en]

    Pricing Asian options is often done using bi- or trinomial lattice methods. Here some results for generalizing these methods to lattices with more nodes are presented. We consider Asian option pricing on a lattice where the underlying asset follows Merton–Bates jump-diffusion model and describe the construction of a lattice using the moment matching technique which results in an equation system described by a rectangular Vandermonde matrix. The system is solved using the explicit expression for the inverse of the Vandermonde matrix and some restrictions on the jump sizes of the lattice and the distribution of moments are identified. The consequences of these restrictions for the suitability of the multinomial lattice methods are also discussed.

  • 80.
    Ostoja-Starzewski, Martin
    et al.
    University of Illinois at Urbana-Champaign, USA.
    Shen, Lihua
    Capital Normal University, Beijing, China.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Tensor random fields in conductivity and classical or microcontinuum theories2015In: Mathematics and mechanics of solids, ISSN 1081-2865, E-ISSN 1741-3028, Vol. 20, no 4, p. 418-432Article in journal (Refereed)
    Abstract [en]

    We study the basic properties of tensor random fields (TRFs) of the wide-sense homogeneous and isotropic kind with generally anisotropic realizations. Working within the constraints of small strains, attention is given to antiplane elasticity, thermal conductivity, classical elasticity and micropolar elasticity, all in quasi-static settings albeit without making any specific statements about the Fourier and Hooke laws. The field equations (such as linear and angular momentum balances and strain–displacement relations) lead to consequences for the respective dependent fields involved. In effect, these consequences are restrictions on the admissible forms of the correlation functions describing the TRFs.

  • 81.
    Ouoba, Mahamadi
    Mälardalen University, School of Education, Culture and Communication.
    Asymptotic expansion of the expected discounted penalty function in a two-scalestochastic volatility risk model.2014Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In this Master thesis, we use a singular and regular perturbation theory to derive

    an analytic approximation formula for the expected discounted penalty function.

    Our model is an extension of Cramer–Lundberg extended classical model because

    we consider a more general insurance risk model in which the compound Poisson

    risk process is perturbed by a Brownian motion multiplied by a stochastic volatility

    driven by two factors- which have mean reversion models. Moreover, unlike

    the classical model, our model allows a ruin to be caused either by claims or by

    surplus’ fluctuation.

    We compute explicitly the first terms of the asymptotic expansion and we show

    that they satisfy either an integro-differential equation or a Poisson equation. In

    addition, we derive the existence and uniqueness conditions of the risk model with

    two stochastic volatilities factors.

  • 82.
    Poljak, D.
    et al.
    University of Split, Split, Croatia.
    Grassi, F.
    Politecnico di Milano, Milano, Italy.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Tkachenko, S.
    Otto-von-Guericke Universität, Magdeburg, Germany.
    Advanced Modeling in Stochastic Computational Electromagnetics: Editorial2018In: Mathematical Problems in Engineering, ISSN 1024123X, Vol. 2018, p. 1-2, article id 8010743Article in journal (Refereed)
  • 83.
    Possolo, Antonio
    et al.
    NIST, Gaithersburg, USA..
    Bodnar, Olha
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Phys Tech Bundesanstalt, Berlin, Germany; NIST, Gaithersburg, USA..
    Butler, Therese A.
    NIST, Gaithersburg, USA..
    Molloy, John L.
    NIST, Gaithersburg, USA..
    Winchester, Michael R.
    NIST, Gaithersburg,USA..
    Value assignment and uncertainty evaluation for single-element reference solutions2018In: Metrologia, ISSN 0026-1394, E-ISSN 1681-7575, Vol. 55, no 3, p. 404-413Article in journal (Refereed)
    Abstract [en]

    A Bayesian statistical procedure is proposed for value assignment and uncertainty evaluation for the mass fraction of the elemental analytes in single-element solutions distributed as NIST standard reference materials. The principal novelty that we describe is the use of information about relative differences observed historically between the measured values obtained via gravimetry and via high-performance inductively coupled plasma optical emission spectrometry, to quantify the uncertainty component attributable to between-method differences. This information is encapsulated in a prior probability distribution for the between-method uncertainty component, and it is then used, together with the information provided by current measurement data, to produce a probability distribution for the value of the measurand from which an estimate and evaluation of uncertainty are extracted using established statistical procedures.

  • 84.
    Radeschnig, David
    Mälardalen University, School of Education, Culture and Communication.
    Modelling Implied Volatility of American-Asian Options: A Simple Multivariate Regression Approach2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This report focus upon implied volatility for American styled Asian options, and a least squares approximation method as a way of estimating its magnitude. Asian option prices are calculated/approximated based on Quasi-Monte Carlo simulations and least squares regression, where a known volatility is being used as input. A regression tree then empirically builds a database of regression vectors for the implied volatility based on the simulated output of option prices. The mean squared errors between imputed and estimated volatilities are then compared using a five-folded cross-validation test as well as the non-parametric Kruskal-Wallis hypothesis test of equal distributions. The study results in a proposed semi-parametric model for estimating implied volatilities from options. The user must however be aware of that this model may suffer from bias in estimation, and should thereby be used with caution.

  • 85.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Mathematical modelling with applications in antenna theory, EMC and actuarial mathematics: SoftCOM 2018 Tutorial2018Conference paper (Refereed)
    Abstract [en]

    Tutorial describes some approaches to mathematical modelling of physical problems. Applications will be illustarted on examples from the areas of antenna theory, grounding systems analysis, modelling of discharge currents and actuarial mathematics. 

    We start with problems related to numerical analysis of sources in presence of a lossy medium. A well-known problem of dealing with so-called Sommerfeld type integrals occurs in these analysis. Their approximate evaluation has been of great interest for researchers in the areas of antenna theory and grounding systems analysis. These integrals arise in the expressions describing the electromagnetic field in the surroundings of such structures when they are located above/inside a semi-conducting media. The fact that these integrals don’t have a closed form solution, enticed researchers to approximately evaluate them either by employing a numerical integration technique, or using some kind of procedure that will approximate them and allow their analytical evaluation. 

    Second part of the tutorial deals with modelling of lightning and electrostatic discharge currents. A general function that would be able to reproduce desired waveshapes of theses currents is needed, such that analytical solutions for their derivatives, integrals, and integral transformations, exist. We present a review of existing models, their advatages and disadvartages and possible extensions. 

    Finally, we discuss modelling of mortality rates of living organisms or equipment. 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. We review existing models and discuss their properties and application to mortality forcasting and pricing life insurances. 

  • 86. Rybakov, Artem
    Volatility prediction and straddle strategy on FORTS market2011In: Exploring the world of financial engineering / [ed] Jevgenijs Carkovs, Anatoliy Malyarenko, Kalev Pärna, Västerås: Mälardalen University , 2011, p. 80-86Chapter in book (Other academic)
    Abstract [en]

    A dynamic one-day-ahead RTS index volatility prediction is applied to straddle (volatility trading) strategy. Clustering effect is employed to detect arbitrage opportunities. The half of the signals generated allows to gain profit from transactions.

  • 87.
    Röman, Jan
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Analytical Finance: Volume I: The Mathematics of Equity Derivatives, Markets, Risk and Valuation2017 (ed. 1)Book (Refereed)
  • 88.
    Röman, Jan
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Analytical Finance: Volume II: The Mathematics of Interest Rate Derivatives, Markets, Risk and Valuation2017 (ed. 1)Book (Refereed)
  • 89.
    Schyberg, Oskar
    Mälardalen University, School of Education, Culture and Communication.
    Monte Carlo Study of Reinsurance Contracts2013Licentiate thesis, monograph (Other academic)
    Abstract [en]

    This thesis is based on three articles concerning to experimental softwarefor evaluation of reinsurance contracts. In paper A we describe and usethe reinsurance analyser (ReAn), an open-source software for analysis ofreinsurance contacts. Moreover, we discuss experimental results, especiallythe risk comparison of excess-of-loss and largest claims reinsurance treaties.In paper B we expand the software including a new excess-of-loss treaty withupper limit. We perform experimental studies comparing extreme value andexcess-of-loss reinsurance treaties. In paper C, we perform a more in depthpresentation of the software. We introduce new treaties as combinations ofstandard treaties. Experimental comparisons are made between these treatiesand other extreme value treaties.

  • 90.
    Schyberg, Oskar
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication.
    Analysis of Reinsurance Processes Using Monte Carlo Based Software2011In: Proceedings ASMDA 2011 / [ed] R. Manca, 2011, p. 878-885Conference paper (Refereed)
  • 91.
    Schyberg, Oskar
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication.
    Monte Carlo Based Software for Analysis of Reinsurance Processes2010In: Proceedings of the International Symposium on Stochastic Models in Reliability Engineering, Life Sciences and Operations Management: SCE—Shamoon College of Engineering, Beer Sheva, February 8–11, 2010 / [ed] Ilia Frenkel et al, Beer Sheva, 2010, p. 975-984Conference paper (Refereed)
  • 92.
    Silvestrov, D.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Jonsson, H.
    Mälardalen University, Department of Mathematics and Physics.
    Stenberg, F.
    Mälardalen University, Department of Mathematics and Physics.
    Convergence of option rewards for Markov type price processes2007In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 13(29), no 4, p. 189-200Article in journal (Other (popular science, discussion, etc.))
    Abstract [en]

    General condition of convergence are given for optimal rewards of American type options for perturbed Markopv type price processes controlled by market stochastic indices

  • 93.
    Silvestrov, D.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Jönsson, H.
    Mälardalen University, Department of Mathematics and Physics.
    Stanberg, F.
    Mälardalen University, Department of Mathematics and Physics.
    Convergence of Option Rewards for Markov Type Price Processes Controlled by Stochastic Indicies. 12006Report (Other academic)
    Abstract [en]

    Conditions of convergence for optimal expected rewards of American type options are given for perturbed Markov type price processes controlled by stochstic indices

  • 94.
    Silvestrov, D.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Teugels, J.
    Masol, V.
    Mälardalen University, Department of Mathematics and Physics.
    Malyarenko, A.
    Mälardalen University, Department of Mathematics and Physics.
    Reinsurance analyser2006In: International Conference Modern Stochastics: Theory and Applications, Kiev, June 19--23, 2006: abstract of communication, 2006, p. page 245-Conference paper (Other academic)
    Abstract [en]

    A program system for analysis and comparison of reincurance contracts is presented.

  • 95.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.
    American-Type Options, Stochastic Approximation Methods, Volume 22015Book (Refereed)
  • 96.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.
    American-Type Options:  Stochastic Approximation Methods. Volume I2014Book (Refereed)
  • 97.
    Silvestrov, Dmitrii
    Mälardalen University, Department of Mathematics and Physics.
    Asymptotic expansions for distributions of the surplus prior and at the time of ruin2007In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 13(29), no 4, p. 183-188Article in journal (Refereed)
    Abstract [en]

    Exponential asymptotic expansion for distributions of the surplus prior and at the time of ruin are given for perturbed risk processes

  • 98.
    Silvestrov, Dmitrii
    Mälardalen University, Department of Mathematics and Physics.
    Asymptotic expansions for quasi-stationary distributions of nonlinearly perturbed semi-Markov processes2007In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 13(29), no 1-2, p. 267-271Article in journal (Refereed)
    Abstract [en]

    Asymptotic expansions for quasi-stationary distributions of nonlinearly perturbed semi-Markov processes are given

  • 99.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication.
    Convergence in Skorokhod J-topology for compositions of stochastic processes2008In: Theory Stoch. Process., ISSN 0321-3900, Vol. 14, no 1, p. 126-143Article in journal (Refereed)
    Abstract [en]

    A survey on functional limit theorems for compositions of stochastic processes ispresented. Applications to stochastic processes with random scaling of time, randomsums, extremes with random sample size, generalised exceeding processes, sum- andmax-processes with renewal stopping, and shock processes are discussed.

  • 100.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.
    Improved Asymptotics for Ruin Probabilities2014In: Modern Problems in Insurance Mathematics / [ed] Silvestrov, Dmitrii; Martin-Löf, Anders, Springer International Publishing , 2014, p. 37-68Chapter in book (Refereed)
    Abstract [en]

    This chapter presents a survey of results on improved asymptotics for ruin probabilities in the Cramér–Lundberg, diffusion, and stable approximations of ruin probabilities for perturbed risk processes, obtained by the author and his collaborators. These results are: exponential asymptotic expansions for ruin probabilities in the Cramér–Lundberg and diffusion approximations of ruin probabilities; necessary and sufficient conditions for convergence of ruin probabilities in the model of diffusion and stable approximations; and explicit exponential rates of convergence in the Cramér–Lundberg approximation for ruin probabilities for reinsurance risk processes.

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