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• 51.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Functional limit theorems for multiparameter fractional Brownian motion2006Ingår i: Journal of theoretical probability, ISSN 0894-9840, E-ISSN 1572-9230, Vol. 19, nr 2, s. 263-288Artikel i tidskrift (Refereegranskat)

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

• 52.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Invariant random fields in vector bundles and application to cosmology2011Ingår i: Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, ISSN 0246-0203, Vol. 47, nr 4, s. 1068-1095Artikel i tidskrift (Refereegranskat)

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

• 53.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Invariant random fields in vector bundles and application to cosmologyManuskript (preprint) (Övrigt vetenskapligt)

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.

• 54.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Invariant random fields on spaces with a group action2013Bok (Refereegranskat)

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.

• 55.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Lectures on cubature methods in financial engineering2011Ingår i: Exploring the world of financíal engineering / [ed] Jeegenijs Carkovs, Anatoliy Malyarenko, Kalev Pärna, Västerås: Mälardalen University , 2011, s. 48-65Kapitel i bok, del av antologi (Övrigt vetenskapligt)

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.

• 56.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Spectral expansions of cosmological fields2015Ingår i: Journal of Statistical Science and Application, ISSN 2328-224X, Vol. 3, nr 11-12, s. 175-193Artikel i tidskrift (Refereegranskat)

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.

• 57.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Spectral expansions of random sections of homogeneous vector bundles2017Ingår i: Teoriya Imovirnostei ta Matematychna Statystyka (THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS ), ISSN 0868-6904, Vol. 97, s. 142-156Artikel i tidskrift (Refereegranskat)

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.

• 58.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Spectral expansions of tensor-valued random fields2017Ingår i: AIP Conference Proceedings, Volume 1798, American Institute of Physics (AIP), 2017, Vol. 1798, s. 1-10, artikel-id 020095Konferensbidrag (Refereegranskat)

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.

• 59.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Option pricing and model calibration under multifactor stochastic volatility and stochastic interest rate - an asymptotic expansion approach2017Ingår i: Proceedings ASMDA2017 / [ed] Skiadas, Christos H., ISAST: International Society for the Advancement of Science and Technology , 2017, s. 219-231-Konferensbidrag (Refereegranskat)

Among other limitations, the celebrated Black--Scholes option pricingmodel assumes constant volatility and constant interest rates, which is not supportedby empirical studies on for example implied volatility surfaces. Studiesby many researchers such as Heston in 1993, Christoffersen in 2009, Fouque in2012, Chiarella--Ziveyi in 2013, and the authors' previous work removed the constantvolatility assumption from the Black--Scholes model by introducing one ortwo stochastic volatility factors with constant interest rate. In the present paperwe follow this line but generalize the model by considering also stochasticinterest rate. More specifically, the underlying asset process is governed by amean-reverting interest rate process in addition to two mean-reverting stochasticvolatility processes of fast and slow mean-reverting rates respectively. The focusis to derive an approximating formula for pricing the European option using adouble asymptotic expansion method.

• 60.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Wichita State University.
Time-Varying Isotropic Vector Random Fields on Compact Two-Point Homogeneous SpacesManuskript (preprint) (Övrigt vetenskapligt)

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.

• 61.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Faculty of Sciences, Department of Mathematics and Computer Sciences,Eduardo Mondlane University, Box 257, Maputo, Mozambique. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Advanced Monte Carlo pricing of European options in a market model with two stochastic volatilities2018Ingår i: 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, s. 409-422Konferensbidrag (Refereegranskat)

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.

• 62.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
University of Illinois at Urbana-Champaign, Urbana, United States.
Random fields related to the symmetry classes of second-order symmetric tensors2018Ingår i: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Springer, 2018, Vol. 271, s. 173-185Kapitel i bok, del av antologi (Refereegranskat)

Under the change of basis in the three-dimensional space by means of an orthogonal matrix g, a matrix A of a linear operator is transformed as A → gAg-1 Mathematically, the stationary subgroup of a symmetric matrix under the above action can be either (Formula Presented), when all three eigenvalues of A are different, or (Formula Presented), when two of them are equal, or O(3), when all three eigenvalues are equal. Physically, one typical application relates to dependent quantities like a second-order symmetric stress (or strain) tensor. Another physical setting is that of dependent fields, such as conductivity with such three cases is the conductivity (or, similarly, permittivity, or anti-plane elasticity) second-rank tensor, which can be either orthotropic, transversely isotropic, or isotropic. For each of the above symmetry classes, we consider a homogeneous random field taking values in the fixed point set of the class that is invariant with respect to the natural representation of a certain closed subgroup of the orthogonal group. Such fields may model stochastic heat conduction, electric permittivity, etc. We find the spectral expansions of the introduced random fields.

• 63.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
University of Illinois at Urbana-Champaign, US.
A Random Field Formulation of Hooke’s Law in All Elasticity Classes2017Ingår i: Journal of elasticity, ISSN 0374-3535, E-ISSN 1573-2681, Vol. 127, nr 2, s. 269-302Artikel i tidskrift (Refereegranskat)

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.

• 64.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
University of Illinois at Urbana-Champaign, USA.
A random field formulation of Hooke’s law in all elasticity classesManuskript (preprint) (Övrigt vetenskapligt)

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.

• 65.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
University of Illinois at Urbana-Champaign, USA.
Fractal planetary rings: energy inequalities and random field model2017Ingår i: International Journal of Modern Physics B, ISSN 0217-9792, Vol. 31, nr 30, artikel-id 1750236Artikel i tidskrift (Refereegranskat)

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.

• 66.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
University of Illinois at Urbana-Champaign, Champaign, United States .
Spectral Expansion of Three-Dimensional Elasticity Tensor Random Fields2016Ingår i: Engineering Mathematics I: Electromagnetics, Fluid Mechanics, Material Physics and Financial Engineering / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016, s. 281-300Kapitel i bok, del av antologi (Refereegranskat)

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.

• 67.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
University of Illinois at Urbana-Champaign.
Spectral expansions of homogeneous and isotropic tensor-valued random fields2016Ingår i: Zeitschrift für angewandte Matematik und Physik ZAMP, ISSN 1420-9039, Vol. 67, nr 3, artikel-id 59Artikel i tidskrift (Refereegranskat)

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.

• 68.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
University of Illinois at Urbana-Champaign.
Statistically isotropic tensor random fields: correlation structures2014Ingår i: Mathematics and Mechanics of Complex Systems, ISSN 2325-3444, Vol. 2, nr 2, s. 209-231Artikel i tidskrift (Refereegranskat)

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.

• 69.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
University of Illinois at Urbana-Champaign.
Tensor Random Fields in Continuum Mechanics2018Ingår i: Encyclopedia of Continuum Mechanics / [ed] Altenbach, Holm and Öchsner, Andreas, Berlin, Heidelberg: Springer Berlin/Heidelberg, 2018, s. 1-9Kapitel i bok, del av antologi (Refereegranskat)
• 70.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
University of Illinois at Urbana-Champaign, USA.
Tensor-Valued Random Fields for Continuum Physics2018Bok (Refereegranskat)
• 71.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
University of Illinois at Urbana-Champaign, USA.
Tensor-Valued Random Fields in Continuum Physics2016Ingår i: Materials with internal structure: Multiscale and Multifield Modeling and Simulation / [ed] P. Trovalusci, Berlin/Heidelberg: Springer Science+Business Media B.V., 2016, s. 75-88Kapitel i bok, del av antologi (Refereegranskat)

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.

• 72.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
University of Illinois in Urbana-Champaign, USA.
The spectral expansion of the elasticity random field2014Ingår i: AIP Conference Proceedings 1637 / [ed] S. Sivasundaram, 2014, s. 647-655Konferensbidrag (Refereegranskat)

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.

• 73.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
University of Illinois at Urbana-Champaign, USA.
Towards stochastic continuum damage mechanicsIngår i: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146Artikel i tidskrift (Refereegranskat)

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.

• 74.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Swedbank, Sweden. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Sensitivity Analysis of Catastrophe Bond Priceunder the Hull–White Interest Rate Model2016Ingår i: Engineering Mathematics I: Electromagnetics, Fluid Mechanics, Material Physics and Financial Engineering / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016Kapitel i bok, del av antologi (Refereegranskat)

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.

• 75.
Mälardalens högskola, Institutionen för matematik och fysik.
Mälardalens högskola, Institutionen för matematik och fysik. Mälardalens högskola, Institutionen för matematik och fysik.
Stochastic modelling of insurance business with dynamical control of investments2004Ingår i: 6th World Congress of Bernoulli Society for Mathematical Statistics and Probability, Barcelona, July 26--31 2004, 2004, s. page 181-Konferensbidrag (Övrigt vetenskapligt)
• 76.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Eastern European University, Lutsk, Ukraine.
Mälardalens högskola, Akademin för ekonomi, samhälle och teknik, Framtidens energi.
Looking for Patterns in Residential Electricity Consumption2014Ingår i: Energy Procedia, ISSN 1876-6102, E-ISSN 1876-6102, Vol. 61, s. 1768-1771Artikel i tidskrift (Refereegranskat)

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.

• 77.
Universit´a di Roma La Sapienza, Italy.
Mälardalens högskola, Institutionen för matematik och fysik. Mälardalens högskola, Institutionen för matematik och fysik.
Homogeneous backward semi-Markov reward models for insurance contracts2005Ingår i: Proceedings of ASMDA 2005 Conference: Brest, 2005, 2005, s. 959-967Konferensbidrag (Övrigt vetenskapligt)

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

• 78.
Islamic Azad University, Science and Research Branch, Saveh, Iran .
Kharazmi University, Tehran, Iran. Islamic Azad University, Karaj Branch, Iran. Sufi Razi, Zanjan, Iran.
Optimisation of the Inflationary Inventory Control Model under Stochastic Conditions with Simpson Approximation: Particle Swarm Optimisation Approach2015Ingår i: Iranian Journal of Management Studies, ISSN 2008-7055, Vol. 8, nr 2, s. 203-220Artikel i tidskrift (Refereegranskat)
• 79.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, Busitema University, Kampala, Uganda.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. College of Natural Science, Makerere University, Kampala, Uganda. College of Natural Science, Makerere University, Kampala, Uganda.
Optimization of the Wishart Joint Eigenvalue Probability Density Distribution Based on the Vandermonde Determinant.Manuskript (preprint) (Övrigt vetenskapligt)

A number of models from mathematics, physics, probability theory and statistics can be described in terms of Wishart matrices and their eigenvalues. The most prominent example being the Laguerre ensembles of the spectrum of Wishart matrix. We aim to express extreme points of the joint eigenvalue probability densitydistribution of a Wishart matrix using optimisation techniques for the Vandermondedeterminant over certain surfaces implicitly defined by univariate polynomials.

• 80.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Lie symmetries of the Black-Scholes type equations in financial mathematics2017Ingår i: Proceedings ASMDA2017 / [ed] Skiadas, Christos H., ISAST: International Society for the Advancement of Science and Technology , 2017Konferensbidrag (Refereegranskat)

In this paper, we consider a two-dimensional Black--Scholes model of financial mathematics. Using Lie theory, we determine the generators of the symmetrygroup of the corresponding Feynman--Kac partial differential equation.

• 81.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Modelling electricity price series using regime-switching GARCH model2015Ingår i: 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, s. 713-725Konferensbidrag (Refereegranskat)

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.

• 82.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Asymptotically Improper Perturbed Renewal Equations: Asymptotic Results and Their Applications2011Rapport (Övrigt vetenskapligt)

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.

• 83.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Exponential asymptotical expansions for ruin probability in a classical risk process with non-polynomial perturbations2014Ingår i: Modern Problems in Insurance Mathematics / [ed] Silvestrov, D., Martin-Löf, A. (eds), Springer, 2014, s. 69-94Kapitel i bok, del av antologi (Refereegranskat)

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.

• 84.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
NONLINEARLY PERTURBED RENEWAL EQUATIONS: THE NON-POLYNOMIAL CASE2012Ingår i: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 84, s. 117-129Artikel i tidskrift (Refereegranskat)

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.

• 85.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Perturbed Renewal Equations with Non-Polynomial Perturbations2010Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)

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.

• 86.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Approximation Methods of European Option Pricing in Multiscale Stochastic Volatility Model2017Ingår i: 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, s. 020112-1-020112-10, artikel-id 020112Konferensbidrag (Refereegranskat)

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.

• 87.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Exponential asymptotics for nonlinearly perturbed renewal equation with non-polynomial perturbations2008Ingår i: Journal of Numerical and Applied Mathematics, ISSN 0868-6912, Vol. 96, nr 1, s. 173-197Artikel i tidskrift (Refereegranskat)

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.

• 88.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. University of Nairobi, Kenya.
Pricing Asian Options using Moment Matching on a Multinomial Lattice2014Ingår i: 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, s. 759-765Konferensbidrag (Refereegranskat)

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.

• 89.
University of Illinois at Urbana-Champaign, USA.
Capital Normal University, Beijing, China. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Tensor random fields in conductivity and classical or microcontinuum theories2015Ingår i: Mathematics and mechanics of solids, ISSN 1081-2865, E-ISSN 1741-3028, Vol. 20, nr 4, s. 418-432Artikel i tidskrift (Refereegranskat)

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.

• 90.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Asymptotic expansion of the expected discounted penalty function in a two-scalestochastic volatility risk model.2014Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)

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.

• 91.
University of Split, Split, Croatia.
Politecnico di Milano, Milano, Italy. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Otto-von-Guericke Universität, Magdeburg, Germany.
Advanced Modeling in Stochastic Computational Electromagnetics: Editorial2018Ingår i: Mathematical Problems in Engineering, ISSN 1024123X, Vol. 2018, s. 1-2, artikel-id 8010743Artikel i tidskrift (Refereegranskat)
• 92.
NIST, Gaithersburg, USA..
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Phys Tech Bundesanstalt, Berlin, Germany; NIST, Gaithersburg, USA.. NIST, Gaithersburg, USA.. NIST, Gaithersburg, USA.. NIST, Gaithersburg,USA..
Value assignment and uncertainty evaluation for single-element reference solutions2018Ingår i: Metrologia, ISSN 0026-1394, E-ISSN 1681-7575, Vol. 55, nr 3, s. 404-413Artikel i tidskrift (Refereegranskat)

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.

• 93.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Modelling Implied Volatility of American-Asian Options: A Simple Multivariate Regression Approach2015Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)

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.

• 94.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mathematical modelling with applications in antenna theory, EMC and actuarial mathematics: SoftCOM 2018 Tutorial2018Konferensbidrag (Refereegranskat)

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.

• 95. Rybakov, Artem
Volatility prediction and straddle strategy on FORTS market2011Ingår i: Exploring the world of financial engineering / [ed] Jevgenijs Carkovs, Anatoliy Malyarenko, Kalev Pärna, Västerås: Mälardalen University , 2011, s. 80-86Kapitel i bok, del av antologi (Övrigt vetenskapligt)

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.

• 96.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Analytical Finance: Volume I: The Mathematics of Equity Derivatives, Markets, Risk and Valuation2017 (uppl. 1)Bok (Refereegranskat)
• 97.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Analytical Finance: Volume II: The Mathematics of Interest Rate Derivatives, Markets, Risk and Valuation2017 (uppl. 1)Bok (Refereegranskat)
• 98.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Monte Carlo Study of Reinsurance Contracts2013Licentiatavhandling, monografi (Övrigt vetenskapligt)

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.

• 99.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Analysis of Reinsurance Processes Using Monte Carlo Based Software2011Ingår i: Proceedings ASMDA 2011 / [ed] R. Manca, 2011, s. 878-885Konferensbidrag (Refereegranskat)
• 100.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Monte Carlo Based Software for Analysis of Reinsurance Processes2010Ingår i: 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, s. 975-984Konferensbidrag (Refereegranskat)
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