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  • 1. Boulougari, Andromachi
    et al.
    Lundengård, Karl
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    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.
    Strass, Belinda
    Application of a power-exponential function-based model to mortality rates forecasting2019In: Communications in Statistics: Case Studies, Data Analysis and Applications, E-ISSN 2373-7484, Vol. 5, no 1, p. 3-10Article in journal (Refereed)
    Abstract [en]

    There are many models for mortality rates. A well-known problem that complicates modeling of human mortality rates is the “accident hump” occurring in early adulthood. Here, two models of mortality rate based on power-exponential functions are presented and compared to a few other models. The models will be fitted to known data of measured death rates from several different countries using numerical techniques for curve-fitting with the nonlinear least-squares method. The properties of the model with respect to forecasting with the Lee–Carter method will be discussed.

  • 2.
    Canhanga, Betuel
    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.
    Murara, Jean-Paul
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ni, Ying
    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.
    Numerical Studies on Asymptotics of European Option under Multiscale Stochastic Volatility2015In: 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. 53-66Conference paper (Refereed)
    Abstract [en]

    Multiscale stochastic volatilities models relax the constant volatility assumption from Black-Scholes option pricing model. Such model can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. Christoffersen et al. [3] presented a model where the underlying priceis governed by two volatility components, one changing fast and another changing slowly. Chiarella and Ziveyi [2] transformed Christoffersen’s model and computed an approximate formula for pricing American options. They used Duhamel’s principle to derive an integral form solution of the boundary value problem associated to the option price. Using method of characteristics, Fourier and Laplace transforms, they obtained with good accuracy the American options prices. In a previous research of the authors (Canhanga et al. [1]), a particular case of Chiarella and Ziveyi [2] model is used for pricing of European options. The novelty of this earlier work is to present an asymptotic expansion for the option price. The present paper provides experimental and numerical studies on investigating the accuracy of the approximation formulae given by this asymptotic expansion. We present also a procedure for calibrating the parameters produced by our first-order asymptotic approximation formulae. Our approximated option prices will be compared to the approximation obtained by Chiarella and Ziveyi [2].

    1. Canhanga B., Malyarenko, A., Ni, Y. and Silvestrov S. Perturbation methods for pricing European options in a model with two stochastic volatilities. 3rd SMTDA Conference Proceedings. 11-14 June 2014, Lisbon Porturgal, C. H. Skiadas (Ed.) 489-500 (2014).

    2. Chiarella, C, and Ziveyi, J. American option pricing under two stochastic volatility processes. J. Appl. Math. Comput. 224:283–310 (2013).

    3. Christoffersen, P.; Heston, S.; Jacobs, K. The shape and term structure of the index option smirk: why multifactor stochastic volatility models work so well. Manage. Sci. 55 (2) 1914-1932; (2009).

  • 3.
    Elchinger, O.
    et al.
    Laboratoire de Mathématiques, Informatique et Applications, Université de Haute Alsace, Mulhouse, France.
    Lundengård, Karl
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Makhlouf, A.
    Laboratoire de Mathématiques Informatique et Applications, Université de Haute Alsace, Mulhouse, France.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Brackets with (τ,σ)-derivations and (p,q)-deformations of Witt and Virasoro algebras2016In: Forum mathematicum, ISSN 0933-7741, E-ISSN 1435-5337, Vol. 28, no 4, p. 657-673Article in journal (Refereed)
    Abstract [en]

    The aim of this paper is to study some brackets defined on (τ,σ)-derivations satisfying quasi-Lie identities. Moreover, we provide examples of (p, q)-deformations of Witt and Virasoro algebras as well as sl(2) algebra. These constructions generalize the results obtained by Hartwig, Larsson and Silvestrov on σ-derivations, arising in connection with discretizations and deformations of algebras of vector fields.

  • 4.
    Javor, V.
    et al.
    University of Niš, Faculty of Electronic Engineering, Niš, Serbia.
    Javor, D.
    University of Niš, Faculty of Electronic Engineering, Niš, Serbia.
    Lundengård, Karl
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    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 of measured lightning discharge currents to tall towers2017In: Conference Proceedings - 2017 17th IEEE International Conference on Environment and Electrical Engineering and 2017 1st IEEE Industrial and Commercial Power Systems Europe, EEEIC / I and CPS Europe 2017, Institute of Electrical and Electronics Engineers Inc. , 2017, article id 7977795Conference paper (Refereed)
    Abstract [en]

    Lightning discharge currents and their derivatives have been measured at instrumented tall towers for a few decades already. Results of those measurements are used for lightning research purposes, modelling of lightning discharges and making improvements in lightning protection. Some of the measured lightning currents are represented in this paper by the multi-peaked analytically extended function (MP-AEF). The same function may be used for lightning current derivatives, thus providing their analytical integration. 

  • 5.
    Javor, Vesna
    et al.
    University of Nis, Faculty of Electronic Eng., Serbia.
    Lundengård, Karl
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Modeling of Artificially-Triggered Lightning Currents by Multi-Peaked Analytically Extended Functions2018In: Compel, ISSN 0332-1649, Vol. 37, no 4, p. 1354-1365Article in journal (Refereed)
    Abstract [en]

    Purpose: This paper aims to present the approximation of lightning currents waveshapes by the multi-peaked analytically extended function (MP-AEF) for the experimentally measured channel-base currents in the artificially triggered lightning discharges. Modified transmission line model of lightning return strokes having the channel current both linearly decaying and sinusoidally changing with height (MTLSIN) is used to calculate the lightning electromagnetic field. Design/methodology/approach: MP-AEF’s parameters for the artificially triggered lightning channel-base currents are calculated by using Marquardt least squares method (MLSM). Lightning electromagnetic fields are calculated based on electromagnetic theory relations, thin-wire antenna model of the vertical lightning channel and the assumption of the perfectly conducting ground. MTLSIN model as an engineering model of lightning strokes is used to obtain the electric field results as these are simultaneously measured in rocket-triggered lightning experiments together with the channel-base currents. Findings: MP-AEF approximates multi-peaked pulse waveshapes. Some important function parameters are chosen prior to the approximation procedure, such as current peaks and the corresponding time moments of those peaks, which presents an advantage in comparison to other functions. The desired accuracy of approximation is obtained by choosing an adequate number of function terms. MLSM is used for the estimation of unknown parameters. Using MTLSIN model, the influence of the channel height and return stroke speed on the lightning electromagnetic field waveshape is analyzed in this paper. Research limitations/implications: MP-AEF may be used for approximation of various multi-peaked waveshapes. It has no errors in the points of maxima which is important for the lightning protection systems design. MTLSIN model may be validated by using simultaneously measured lightning electromagnetic fields at various distances from the channel and for channel heights estimated in the experiments. It is also possible to approximate measured current derivatives by MP-AEF and use them for further computation. Originality/value: MTLSIN model is proposed in this paper for the evaluation of lightning electromagnetic fields induced by artificially triggered lightning discharges. The procedure is based on the approximation of lightning channel-base currents by the multi-peaked analytically extended function previously proposed by the authors. This function may be used not only for representing lightning currents but also for other waveshapes as current derivatives, electric and magnetic fields and their derivatives, which are all important for the lightning protection design. MTLSIN gives lightning electromagnetic fields results which are in better agreement with measured fields than those obtained by other models from literature.

  • 6.
    Javor, Vesna
    et al.
    Faculty of Electronic Engineering, Department of Power Engineering, University of Niš, Niš 18000, Serbia.
    Lundengård, Karl
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    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.
    Analytical Representation of Measured Lightning Currents and Its Application to Electromagnetic Field Estimation2017In: IEEE transactions on electromagnetic compatibility (Print), ISSN 0018-9375, E-ISSN 1558-187X, ISSN 0018-9375, Vol. 60, no 5, p. 1415-1426Article in journal (Refereed)
    Abstract [en]

    Lightning discharge currents waveshapes and their derivatives with multiple peaks are measured in artificially triggered lightning experiments and at instrumented tall towers. Such waveshapes are represented in this paper by the N-peaked analytically extended function (NP-AEF) and Marquardt least-squares method is applied for the estimation of its nonlinear parameters. Typical channel-base currents of the first negative, subsequent negative strokes, and positive strokes, based on comprehensive measurements by Berger et al. at Monte San Salvatore in Switzerland, are approximated by NP-AEFs and used in the computation of lightning electromagnetic fields. A new attenuation factor introducing nonlinear current attenuation along the channel is applied within the modified transmission line model (MTLSIN). A lightning return stroke is assumed to have a vertical discharge channel at the perfectly conducting ground. In order to validate this model, calculated lightning electromagnetic fields are compared with the typical, as measured by Lin et al. at various distances from the discharges. Lightning currents and their derivatives measured at the tall towers are also approximated by NP-AEFs. For the measured artificially triggered lightning currents, MTLSIN is applied for the calculation of their electromagnetic fields. These are compared with the measured fields of specific lightning strokes, so as to results of other models.

  • 7.
    Javor, Vesna
    et al.
    University of Nis, Faculty of Electronic Eng., Serbia.
    Lundengård, Karl
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    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.
    Application of Genetic Algorithm to Estimation of Function Parameters in Lightning Currents Approximations2017In: International Journal of Antennas and Propagation, ISSN 1687-5869, E-ISSN 1687-5877, Vol. 2017, article id 4937943Article in journal (Refereed)
    Abstract [en]

    Genetic algorithm (GA) is applied for the estimation of two-peaked analytically extended function (2P-AEF) parameters in this paper. 2P-AEF is used for approximation of measured and typical lightning discharge currents. Lightning discharge channel is often modeled as thin-wire vertical antenna at perfectly conducting ground. Engineering lightning stroke models assume that the current along that channel is related to the channel-base current which may be measured at the instrumented tall towers and in triggered lightning experiments. Mathematical modeling of lightning currents is important in verification of lightning strokes models based on simultaneously measured electromagnetic fields at various distances, so as in lightning protection studies, computation of lightning induced effects and simulation of overvoltages in power systems. Typical lightning discharge currents of the first positive, first negative, and subsequent negative strokes are defined by IEC 62305 Standard based on comprehensive measurements. Parameters of 2P-AEF’s approximation of the typical negative first stroke current are determined by GA and compared to approximations obtained by other functions. Measured currents at Monte San Salvatore in Switzerland, at Morro de Cachimbo Station in Brazil, and in rocket-triggered lightning experiments at Camp Blanding in Florida are approximated by 2P-AEFs, and good agreement with experimentally measured waveshapes is obtained.

  • 8.
    Javor, Vesna
    et al.
    University of Nis, Faculty of Electronic Eng., Serbia.
    Lundengård, Karl
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    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.
    Electrostatic discharge currents and their derivatives' approximation by piecewise power-exponential functions2018In: Turkish Journal of Electrical Engineering and Computer Sciences, ISSN 1300-0632, E-ISSN 1303-6203, Vol. 26, no 2, p. 1093-1102Article in journal (Refereed)
    Abstract [en]

    An analytically extended function based on power-exponential functions is used in this paper for approxi- mation of electrostatic discharge (ESD) currents and their derivatives. The Marquardt least-squares method (MLSM) is applied for obtaining nonlinear function parameters. IEC 61000-4-2 Standard ESD current is approximated, as well as some measured ESD currents' wave shapes. Power-exponential terms are extended at the local maxima and minima of the represented wave shape, so that this approximation is done from peak to peak. ESD current derivative is approxi- mated using the same procedure in order to obtain the continuous second order derivative of the current, as all piecewise functions are of differentiability class C1L . Currents and their derivatives are often measured in ESD experiments so that their analytical representation is needed for simulation of ESD phenomena, better definition of standard requirements, and computation of the transient fields and induced effects.

  • 9.
    Javor, Vesna
    et al.
    University of Nis, Faculty of Electronic Eng., Serbia.
    Lundengård, Karl
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    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.
    Measured electrostatic discharge currents modeling and simulation2015In: Proceedings of 12th International Conference on Telecommunication in Modern Satellite, Cable and Broadcasting Services (TELSIKS), 2015 / [ed] Bratislav D. Milovanović, Nebojša S. Dončov, Zoran Ž. Stanković, IEEE conference proceedings, 2015, p. 209-212Conference paper (Refereed)
    Abstract [en]

    Analytically extended function (AEF) for modeling measured electrostatic discharge (ESD) currents is presented in this paper. This function is used for the IEC 61000-4-2 Standard current and AEF parameters are calculated using least-squares method. Procedure of obtaining function parameters is simple for experimentally measured multi-peaked functions, such as lightning and other ESD currents. Simulation of ESD currents is done by simple electric circuits and using MATLAB.

  • 10.
    Javor, Vesna
    et al.
    University of Nis, Faculty of Electronic Eng., Serbia.
    Lundengård, Karl
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    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 of Rocket-Triggered Lightning Currents by Multi-Peaked Analytically Extended Function2017Conference paper (Refereed)
  • 11.
    Lundengård, Karl
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Extreme points of the Vandermonde determinant and phenomenological modelling with power exponential functions2019Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis discusses two topics, finding the extreme points of the Vandermonde determinant on various surfaces and phenomenological modelling using power-exponential functions. The relation between these two problems is that they are both related to methods for curve-fitting. Two applications of the mathematical models and methods are also discussed, modelling of electrostatic discharge currents for use in electromagnetic compatibility and modelling of mortality rates for humans. Both the construction and evaluation of models is discussed.

    In the first chapter the basic theory for later chapters is introduced. First the Vandermonde matrix, a matrix whose rows (or columns) consists of monomials of sequential powers, its history and some of its properties are discussed. Next, some considerations and typical methods for a common class of curve fitting problems are presented, as well as how to analyse and evaluate the resulting fit. In preparation for the later parts of the thesis the topics of electromagnetic compatibility and mortality rate modelling are briefly introduced.

    The second chapter discusses some techniques for finding the extreme points for the determinant of the Vandermonde matrix on various surfaces including spheres, ellipsoids and cylinders. The discussion focuses on low dimensions, but some results are given for arbitrary (finite) dimensions.

    In the third chapter a particular model called the p-peaked Analytically Extended Function (AEF) is introduced and fitted to data taken either from a standard for electromagnetic compatibility or experimental measurements. The discussion here is entirely focused on currents originating from lightning or electrostatic discharges.

    The fourth chapter consists of a comparison of several different methods for modelling mortality rates, including a model constructed in a similar way to the AEF found in the third chapter. The models are compared with respect to how well they can be fitted to estimated mortality rate for several countries and several years and the results when using the fitted models for mortality rate forecasting is also compared.

  • 12.
    Lundengård, Karl
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Generalized Vandermonde matrices and determinants in electromagnetic compatibility2017Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    Matrices whose rows (or columns) consists of monomials of sequential powers are called Vandermonde matrices and can be used to describe several useful concepts and have properties that can be helpful for solving many kinds of problems. In this thesis we will discuss this matrix and some of its properties as well as a generalization of it and how it can be applied to curve fitting discharge current for the purpose of ensuring electromagnetic compatibility.

    In the first chapter the basic theory for later chapters is introduced. This includes the Vandermonde matrix and some of its properties, history, applications and generalizations, interpolation and regression problems, optimal experiment design and modelling of electrostatic discharge currents with the purpose to ensure electromagnetic compatibility.

    The second chapter focuses on finding the extreme points for the determinant for the Vandermonde matrix on various surfaces including spheres, ellipsoids, cylinders and tori. The extreme points are analysed in three dimensions or more.

    The third chapter discusses fitting a particular model called the p-peaked Analytically Extended Function (AEF) to data taken either from a standard for electromagnetic compatibility or experimental measurements. More specifically the AEF will be fitted to discharge currents from the IEC 62305-1 and IEC 61000-4-2 standards for lightning protection and electrostatic discharge immunity as well as some experimentally measured data of similar phenomena.

  • 13.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ogutu, Carolyne
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. University of Nairobi, Kenya.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ni, Ying
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Weke, P.
    University of Nairobi, Kenya.
    Construction of moment-matching multinomial lattices using Vandermonde matrices and Gröbner bases2017In: AIP Conference Proceedings / [ed] Sivasundaram, S, American Institute of Physics (AIP), 2017, Vol. 1798, p. 020094-1-020094-7, article id 020094Conference paper (Refereed)
    Abstract [en]

    In order to describe and analyze the quantitative behavior of stochastic processes, such as the process followed by a financial asset, various discretization methods are used. One such set of methods are lattice models where a time interval is divided into equal time steps and the rate of change for the process is restricted to a particular set of values in each time step. The well-known binomial- and trinomial models are the most commonly used in applications, although several kinds of higher order models have also been examined. Here we will examine various ways of designing higher order lattice schemes with different node placements in order to guarantee moment-matching with the process. 

  • 14.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ogutu, Carolyne
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. University of Nairobi, Nairobi, Kenya.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Weke, Patrick
    University of Nairobi, Nairobi, Kenya.
    Asian Options, Jump-Diffusion Processes on a Lattice, and Vandermonde Matrices2014In: Modern Problems in Insurance Mathematics / [ed] Silvestrov, Dmitrii, Martin-Löf, Anders, Springer International Publishing , 2014, p. 335-363Chapter in book (Refereed)
    Abstract [en]

    Asian options are options whose value depends on the average asset price during its lifetime. They are useful because they are less subject to price manipulations. We consider Asian option pricing on a lattice where the underlying asset follows the Merton–Bates jump-diffusion model. We describe the construction of the lattice using the moment matching technique which results in an equation system described by a Vandermonde matrix. Using some properties of Vandermonde matrices we calculate the jump probabilities of the resulting system. Some conditions on the possible jump sizes in the lattice are also given.

  • 15.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ogutu, Carolyne
    University of Nairobi, Nairobi, Kenya.
    Österberg, Jonas
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ni, Ying
    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, Nairobi, Kenya.
    Moment-matching multinomial lattices using Vandermonde matrices for option pricing2016In: Stochastic and Data Analysis Methods and Applications in Statistics and Demography: Book 2 / [ed] James R. Bozeman, Teresa Oliveira and Christos H. Skiadas, ISAST , 2016, Vol. 2, p. 15-29Conference paper (Refereed)
    Abstract [en]

    Lattice models are discretization methods that divide the life of a financial option into time steps of equal length and model the underlying asset movement at each time step. A financial option of American or European style can be evaluated conveniently via backward induction using a lattice model. The most common lattice models are the well-known binomial- and trinomial lattice models, although severalkinds of higher order models have also been examined in the literature. In the presentpaper we present an explicit scheme for creating a lattice model of arbitrary order and use the Vandermonde matrix to determine suitable parameters. Some selected models created using this scheme are examined with regard to their suitability for option pricing

  • 16.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Javor, Vesna
    University of Niš, Faculty of Electronic Engineering, Niš, Serbia.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    An examination of the multi-peaked analytically extended function for approximation of lightning channel-base currents2016Manuscript (preprint) (Other academic)
    Abstract [en]

    A multi-peaked version of the analytically extended function (AEF) intended for approximation of multi-peaked lightning current wave-forms will be presented along with some of its basic properties. A general framework for estimating the parameters of the AEF using the Marquardt least-squares method (MLSM) for a waveform with an arbitrary (finite) number of peaks as well as a given charge trans-fer and specific energy will also be described. This framework is used to find parameters for some common single-peak wave-forms and some advantages and disadvantages of the approach will be discussed.

  • 17.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Javor, Vesna
    University of Nis, Faculty of Electronic Eng., Serbia.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Application of the Marquardt Least Square Method to the Estimation of Pulse Function Parameters2014In: 10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014Conference date: 15–18 July 2014 Location: Narvik, Norway ISBN: 978-0-7354-1276-7 Editor: Seenith Sivasundaram Volume number: 1637 Published: 10 december 2014, 2014, p. 637-646Conference paper (Refereed)
    Abstract [en]

    Application of the Marquardt least-squares method (MLSM) to the estimation of non-linear parameters of functionsused for representing various lightning current waveshapes is presented in this paper. Parameters are determined for the Pulse,Heidler’s and DEXP function representing the first positive, first and subsequent negative stroke currents as given in IEC62305-1 Standard Ed.2, and also for some other fast- and slow-decaying lightning current waveshapes. The results prove theability of the MLSM to be used for the estimation of parameters of the functions important in lightning discharge modeling.

  • 18.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Javor, Vesna
    University of Niš, Faculty of Electronic Engineering, Niš, Serbia.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Application of the multi-peaked analytically extended function to representation of some measured lightning currents2016In: Serbian Journal of Electrical Engineering, ISSN 1451-4869, Vol. 13, no 2, p. 145-155Article in journal (Refereed)
    Abstract [en]

    A multi-peaked form of the analytically extended function (AEF) is used for approximation of lightning current waveforms in this paper. The AEF function's parameters are estimated using the Marquardt least-squares method (MLSM), and the general procedure for fitting the p-peaked AEF function to a waveform with an arbitrary (finite) number of peaks is briefly described. This framework is used for obtaining parameters of 2-peaked waveforms typically present when measuring first negative stroke currents. Advantages, disadvantages and possible improvements of the approach are also discussed.

  • 19.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Javor, Vesna
    University of Nis, Faculty of Electronic Eng., Serbia.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Electrostatic discharge current modelling using multi-peaked analytically extended function2017In: Proceedings of 2nd International Multidisciplinary Conference on Computer and Energy Science (SpliTech), IEEE conference proceedings, 2017, p. 272-277, article id 8019264Conference paper (Refereed)
    Abstract [en]

    In order to establish realistic requirements for ESD generators used in equipment and device testing, as well as to ensure and improve the repeatability of tests, an analytical expression of real electrostatic discharge (ESD) currents is sought for. It should be adoptable to various test levels, test set-ups and procedures, and also various ESD conditions (approach speeds, types of electrodes, relative arc length, humidity, etc). A mathematical function is necessary for computer simulation of such phenomena, for verification of test generators and for improving standard waveshape definition.

  • 20.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Javor, Vesna
    Univ Nis, Dept Power Engn, Fac Elect Engn, Nish, Serbia..
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Electrostatic discharge currents representation using the analytically extended function with P peaks by interpolation on a D-optimal design2019In: Facta Universitatis Series: Electronics and Energetics, ISSN 0353-3670, Vol. 32, no 1, p. 25-49Article in journal (Refereed)
    Abstract [en]

    In this paper the Analytically Extended Function (AEF) with p peaks is used for representation of the electrostatic discharge (ESD) currents and lightning discharge currents. The fitting to data is achieved by interpolation of certain data points. In order to minimize unstable behaviour, the exponents of the AEF are chosen from a certain arithmetic sequence and the interpolated points are chosen according to a D-optimal design. The method is illustrated using several examples of currents taken from standards and measurements.

  • 21.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Javor, Vesna
    University of Nis, Faculty of Electronic Eng., Serbia..
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Electrostatic Discharge Currents Representation using the Multi-Peaked Analytically Extended Function by Interpolation on a D-Optimal DesignManuscript (preprint) (Other academic)
    Abstract [en]

    Multi-peaked analytically extended function (AEF), previously applied by the authors to modelling of lightning discharge currents, is used in this paper for representation of the electrostatic discharge (ESD) currents. The fitting to data is achieved by interpolation of certain data points. In order to minimize unstable behaviour, the exponents of the AEF are chosen from a certain arithmetic sequence and the interpolated points are chosen according to a D-optimal design. ESD currents' modelling is illustrated through two examples: one corresponding to an approximation of the IEC Standard 61000-4-2 waveshape, and the other to representation of some measured ESD current.

  • 22.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Javor, Vesna
    University of Nis, Faculty of Electronic Eng., Serbia.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Electrostatic Discharge Currents Representation using the Multi-Peaked Analytically Extended Function by Interpolation on a D-Optimal Design2017Conference paper (Refereed)
    Abstract [en]

    Multi-peaked analytically extended function (AEF), previously applied by the authors to modelling of lightning discharge currents, is used in this paper for representation of the electrostatic discharge (ESD) currents. The fitting to data is achieved by interpolation of certain data points. In order to minimize unstable behaviour, the exponents of the AEF are chosen from a certain arithmetic sequence and the interpolated points are chosen according to a D-optimal design. ESD currents’ modelling is illustrated through two examples: one corresponding to an approximation of the IEC Standard 61000-4-2 waveshape, and the other to representation of some measured ESD current. 

  • 23.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Javor, Vesna
    University of Nis, Serbia.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Estimation of Parameters for the Multi-peaked AEF Current Functions2015In: 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. 623-636Conference paper (Refereed)
    Abstract [en]

    Examination of how the analytically extended function (AEF) can be used to approximate multi-peaked lightning current waveforms, is performed in the paper. A general framework for estimating the parameters of the AEF using the Marquardt least-squares method (MLSM) for a waveform with an arbitrary (finite) number of peaks is presented. This framework is used to find parameters for some common waveforms with a single peak, such as one-peaked Standard IEC 62305 lightning currents.

  • 24.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Javor, Vesna
    University of Nis, Faculty of Electronic Eng., Serbia.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Estimation of Parameters for the Multi-peaked AEF Current Functions2017In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 19, no 4, p. 1107-1121Article in journal (Refereed)
    Abstract [en]

    An examination of how the analytically extended function (AEF) can be used to approximate multi-peaked lightning current waveforms, is presented in the paper. A general framework for estimating the parameters of the AEF using the Marquardt least-squares method (MLSM) for a waveform with an arbitrary (finite) number of peaks is presented. This framework is used to find parameters for some common waveforms with a single peak, such as Standard IEC 62305 lightning currents. Illustration of fitting a p-peak AEF to recorded lightning current data is also presented.

  • 25.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Javor, Vesna
    University of Nis, Faculty of Electronic Eng., Serbia.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Estimation of Pulse Function Parameters for Approximating Measured Lightning Currents Using the Marquardt Least Squares Method2014In: IEEE International Symposium on Electromagnetic Compatibility, 2014, p. 571-576Conference paper (Refereed)
    Abstract [en]

    The Marquardt least-squares method is applied in this paper for estimation of the Pulse function’s non-linear para­meters in order to approximate measured lightning currents. Such procedure is generalized so it could be used for other pulse functions representing lightning current waveshapes. The obtai­ned results show that this method provides good results for the IEC 62305-1 standard lightning current waveshapes of the first and subsequent return stroke currents, and also for some measu­red fast- and slow-decaying current waveshapes.

  • 26.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Javor, Vesna
    University of Nis, Faculty of Electronic Eng., Serbia.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Multi-Peaked Analytically Extended Function Representing Electrostatic Discharge (ESD) Currents2017In: AIP Conference Proceedings, Volume 1798 / [ed] Seenith Sivasundaram, American Institute of Physics (AIP), 2017, Vol. 1798, p. 020093-1-020093-10, article id 020093Conference paper (Refereed)
    Abstract [en]

    A multi-peaked analytically extended function (AEF), previously applied by the authors to modeling of lightning dischargecurrents, is used in this paper for representation of the electrostatic discharge (ESD) currents. In order to estimate itsnon-linear parameters, the Marquardt least-squares method (MLSM) is used. ESD currents’ modelling is illustrated through anessential example corresponding to approximation of the IEC Standard 61000-4-2 waveshape.

  • 27.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Javor, Vesna
    University of Nis, Faculty of Electronic Eng., Serbia.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Novel Approach to Modelling of Lightning Current Derivative2017In: Facta Universitatis Series: Electronics and Energetics, ISSN 0353-3670, E-ISSN 2217-5997, Vol. 30, no 2, p. 245-256Article in journal (Refereed)
    Abstract [en]

    A new approach to mathematical modelling of lightning current derivative is proposed in this paper. It builds on the methodology, previously developed by the authors, for representing lightning currents and electrostatic discharge (ESD) currents waveshapes. It considers usage of a multi-peaked form of the analytically extended function (AEF) for approximation of current derivative waveshapes. The AEF function parameters are estimated using the Marquardt least-squares method (MLSM) and the framework for fitting the multi-peaked AEF to a waveshape with an arbitrary number of peaks is briefly described. This procedure is validated performing a few numerical experiments, including fitting the AEF to single- and multi-peaked waveshapes corresponding to measured current derivatives.

  • 28.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Javor, Vesna
    University of Nis, Faculty of Electronic Eng., Serbia.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    On Some Properties of the Multi-Peaked Analytically Extended Function for Approximation of Lightning Discharge Currents2016In: Engineering Mathematics I: Electromagnetics, Fluid Mechanics, Material Physics and Financial Engineering, Series: Springer Proceedings in Mathematics & Statistics / [ed] Sergei Silvestrov, Milica Rančić, Heidelberg: Springer, 2016, p. 151-172Chapter in book (Refereed)
    Abstract [en]

    According to experimental results for lightning discharge currents, they are classified in the IEC 62305 Standard into waveshapes representing the first positive, first and subsequent negative strokes, and long-strokes. These waveshapes, especially shot-term pulses, are approximated with a few mathematical functions in literature, in order to be used in lightning discharge models for calculations of electromagnetic field and lightning induced effects. An analytically extended function (AEF) is presented in this paper and used for lightning currents modeling. The basic properties of this function with a finite number of peaks are examined. A general framework for estimating the parameters of the AEF using the Marquardt least-squares method (MLSM) for a waveform with an arbitrary (finite) number of peaks as well as for the given charge transfer and specific energy is described. This framework is used to find parameters for some common single-peak wave-forms and some advantages and disadvantages of the approach are also discussed.

  • 29.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    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 mortality rates using the powerexponential function2017In: Booklet of abstracts of SPAS2017 - International Conference on Stochastic Processes and Algebraic Structures– From Theory Towards Applications, 2017Conference paper (Refereed)
    Abstract [en]

    There are many models for the mortality rates of humans and other organisms. A phenomenon that complicates the modelling of human mortality rates is a rapid increase in mortality rate for young adults (in western Europe this is especially pronounced at the age of 25). We will examine models for mortality rates based on power-exponential functions, compare them to empirical data for mortality rates and other models.

  • 30.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    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.
    Javor, Vesna
    University of Niš, Niš, Serbien.
    An Examination of the Multi-Peaked Analytically Extended Function for Approximation of Lightning Channel-Base Currents2015In: 12TH INTERNATIONAL CONFERENCE ON APPLIED ELECTROMAGNETICS PES2015: Proceedings of extended abstracts / [ed] Dr Dragan Tasic, Faculty of Electronic Engineering (Niš) , 2015Conference paper (Refereed)
    Abstract [en]

    A multi-peaked version of the analytically extendedfunction (AEF) intended for approximation of multi-peaked light-ning current waveforms will be presented along with some of itsbasic properties. A general framework for estimating the parame-ters of the AEF using the Marquardt least-squares method(MLSM) for a waveform with an arbitrary (finite) number ofpeaks as well as a given charge transfer and specific energy willalso be described. This framework is used to find parameters forsome common single-peak wave-forms and some advantages anddisadvantages of the approach will be discussed.

  • 31.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Österberg, Jonas
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication.
    Extreme points of the Vandermonde determinant on the sphere and some limits involving the generalized Vandermonde determinant2013Report (Other academic)
    Abstract [en]

    The values of the determinant of Vandermonde matrices with real elements are analyzed both visually and analytically over the unit sphere in various dimensions. For three dimensions some generalized Vandermonde matrices are analyzed visually. The extreme points of the ordinary Vandermonde determinant on finite-dimensional unit spheres are given as the roots of rescaled Hermite polynomials and a recursion relation is provided for the polynomial coefficients. Analytical expressions for these roots are also given for dimension three to seven. A transformation of the optimization problem is provided and some relations between the ordinary and generalized Vandermonde matrices involving limits are discussed.

  • 32.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Österberg, Jonas
    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.
    Optimization of the determinant of the Vandermonde matrix and related matrices2014In: 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, American Institute of Physics (AIP), 2014, Vol. 1637, p. 627-636Conference paper (Refereed)
    Abstract [en]

    Various techniques for interpolation of data, moment matching in stochastic applications and various methods in numerical analysis can be described using Vandermonde matrices. For this reason the properties of the determinant of the Vandermonde matrix and related matrices are interesting. Here the extreme points of the Vandermonde determinant, and related determinants, on some simple surfaces such as the unit sphere are analyzed, both numerically and analytically. Some results are also visualized in various dimensions. The extreme points of the Vandermonde determinant are also related to the roots of certain orthogonal polynomials such as the Hermite polynomials.

  • 33.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Österberg, Jonas
    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.
    Optimization of the Determinant of the Vandermonde Matrix and Related Matrices2018In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 20, no 4, p. 1417-1428Article in journal (Refereed)
    Abstract [en]

    The value of the Vandermonde determinant is optimized over various surfaces, including the sphere, ellipsoid and torus. Lagrange multipliers are used to find a system of polynomial equations which give the local extreme points in its solutions. Using Grobner basis and other techniques the extreme points are given either explicitly or as roots of polynomials in one variable. The behavior of the Vandermonde determinant is also presented visually in some interesting cases.

  • 34.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Österberg, Jonas
    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.
    Optimization of the determinant of the Vandermonde matrix on the sphere and related surfaces2015In: 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. 637-648Conference paper (Refereed)
    Abstract [en]

    The value of the Vandermonde determinant is optimized over various surfaces, including the sphere, ellipsoid and torus. Lagrange multipliers are used to find a system of polynomial equations which give the local extreme points in its solutions. Using Gröbner basis and other techniques the extreme points are given either explicitly or as roots of polynomials in one variable. The behavior of the Vandermonde determinant is also presented visually in some interesting cases.

  • 35.
    Muhumuza, Asaph Keikara
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, Busitema University, Kampala, Uganda.
    Lundengård, Karl
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Österberg, Jonas
    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.
    Mango, John
    Department of Mathematics, Makerere University, Kampala, Uganda.
    Kakuba, Godwin
    Department of Mathematics, Makerere University, Kampala, Uganda.
    Extreme points of the Vandermonde determinant on surfaces implicitly determined by a univariate polynomialManuscript (preprint) (Other academic)
    Abstract [en]

    In this paper some results on optimising the Vandermonde determinanton a few different surfaces defined by univariate polynomials are discussed. The coordinates of the extreme points are given as roots of polynomials. Applications in curve-fitting and electrostatics are also briefly discussed.

  • 36.
    Muhumuza, Asaph Keikara
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, Busitema University, Kampala, Uganda.
    Lundengård, Karl
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Österberg, Jonas
    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.
    Mango, John
    College of Natural Science, Makerere University, Kampala, Uganda.
    Kakuba, Goodwin
    College of Natural Science, Makerere University, Kampala, Uganda.
    Optimization of the Wishart Joint Eigenvalue Probability Density Distribution Based on the Vandermonde Determinant.Manuscript (preprint) (Other academic)
    Abstract [en]

    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.

  • 37.
    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.

1 - 37 of 37
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