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  • 1.
    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

  • 2.
    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.

  • 3.
    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.

  • 4.
    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.

  • 5.
    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.

  • 6.
    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.

  • 7.
    Tahvili, Sahar
    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.
    Strategic maintenance planning by fuzzy AHP and Markov Decision Processes2015In: ASMDA 2015 Proceedings: 16th Applied Stochastic Models and Data Analysis International Conference with 4th Demographics 2015 Workshop, ISAST: International Society for the Advancement of Science and Technology , 2015, p. 991-1004Conference paper (Refereed)
    Abstract [en]

    The work of engineering and business professionals includes making a series of decisions and optimizations. Real world decision making problems faced by decision makers (DM) involve multiple, usually conflicting, criteria. These multicriteria decision making problems (MCDM) are usually complicated and large in scale. In strategic Maintenance planning, choices are made on where to focus time and effort, where to spend money. We consider a framework for strategic maintenance planning in a modern maintenance driven organization. Our focus is on a multi-stage framework in which the planning is divided into two stages, identifying an optimal set of possible actions and finding the optimal decision policy for these actions for each point in time as a function of the stochastically evolving system state. To this respect we consider the MCDM method of AHP (Analytical hierarchical programming) in a fuzzy environment, and Markov decision processes (MDP).

  • 8.
    Tahvili, Sahar
    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.
    Biteus, Jonas
    Scania CV, Sweden .
    Solving complex maintenance planning optimization problems using stochastic simulation and multi-criteria fuzzy decision making2014In: 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, American Institute of Physics (AIP), 2014, p. 766-775Conference paper (Refereed)
    Abstract [en]

    One of the most important factors in the operations of many cooperations today is to maximize profit and one important tool to that effect is the optimization of maintenance activities. Maintenance activities is at the largest level divided into two major areas, corrective maintenance (CM) and preventive maintenance (PM). When optimizing maintenance activities, by a maintenance plan or policy, we seek to find the best activities to perform at each point in time, be it PM or CM. We explore the use of stochastic simulation, genetic algorithms and other tools for solving complex maintenance planning optimization problems in terms of a suggested framework model based on discrete event simulation.

1 - 8 of 8
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