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  • 1.
    Aljarbouh, Ayman
    et al.
    Centre de Recherche INRIA, Rennes, France.
    Zeng, Yingfu
    Rice University, Houston, Texas, United States.
    Duracz, Adam
    Högskolan i Halmstad, Akademin för informationsteknologi, Halmstad Embedded and Intelligent Systems Research (EIS), Centrum för forskning om inbyggda system (CERES).
    Caillaud, Benoît
    Centre de Recherche INRIA, Rennes, France.
    Taha, Walid
    Högskolan i Halmstad, Akademin för informationsteknologi, Halmstad Embedded and Intelligent Systems Research (EIS), Centrum för forskning om inbyggda system (CERES). Rice University, Houston, Texas, United States.
    Chattering-Free Simulation for Hybrid Dynamical Systems: Semantics and Prototype Implementation2016Inngår i: 2016 IEEE Intl Conference on Computational Science and Engineering (CSE) and IEEE Intl Conference on Embedded and Ubiquitous Computing (EUC) and 15th Intl Symposium on Distributed Computing and Applications for Business Engineering (DCABES) / [ed] Randall Bilof, Los Alamitos: IEEE Computer Society, 2016, s. 412-422, artikkel-id 7982279Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Chattering is a fundamental phenomenon that is unique to hybrid systems, due to the complex interaction between discrete dynamics (in the form of discrete transitions) and continuous dynamics (in the form of time). In practice, simulating chattering hybrid systems is challenging in that simulation effectively halts near the chattering time point, as an infinite number of discrete transitions would need to be simulated. In this paper, formal conditions are provided for when the simulated models of hybrid systems display chattering behavior, and methods are proposed for avoiding chattering “on the fly” in runtime. We utilize dynamical behavior analysis to derive conditions for detecting chattering without enumeration of modes. We also present a new iterative algorithm to allow for solutions to be carried past the chattering point, and we show by a prototypical implementation how to generate the equivalent chattering-free dynamics internally by the simulator in the main simulation loop. The concepts are illustrated with examples throughout the paper. © 2016 IEEE.

  • 2.
    Antczak, Magdalena
    et al.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Leniec, Marta
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Pricing and Hedging of Defaultable Models2011Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
    Abstract [en]

    Modelling defaultable contingent claims has attracted a lot of interest in recent years, motivated in particular by the Late-2000s Financial Crisis. In several papers various approaches on the subject have been made. This thesis tries to summarize these results and derive explicit formulas for the prices of financial derivatives with credit risk. It is divided into two main parts. The first one is devoted to the well-known theory of modelling the default risk while the second one presents the results concerning pricing of the defaultable models that we obtained ourselves.

  • 3.
    Boguta, Maria
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE).
    A New Space-Time Model for Interacting Agents in the Financial Market2009Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
    Abstract [en]

    In this thesis we present a new space-time model of interacting agents in the financial market. It is a combination of the Curie-Weiss model and a model introduced by Järpe. We investigate properties such as the critical temperature and magnetization of the system. The distribution of the Hamiltonian function is obtained and a hypothesis test of independence is derived. The results are illustrated in an example based on real data.

  • 4.
    Bordag, Ljudmila A.
    Högskolan i Halmstad, Akademin för informationsteknologi, Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    On Option-Valuation in Illiquid Markets: Invariant Solutions to a Nonlinear Model2008Inngår i: Mathematical control theory and finance / [ed] Andrey Sarychev; et al, Berlin: Springer Berlin/Heidelberg, 2008, s. 71-94Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    The present model describes a perfect hedging strategy for a large trader. In this case the hedging strategy affects the price of the underlying security. The feedback-effect leads to a nonlinear version of the Black-Scholes partial differential equation. Using Lie group theory we reduce in special cases the partial differential equation to some ordinary differential equations. The Lie group found for the model equation gives rise to invariant solutions. Families of exact invariant solutions for special values of parameters are described. © 2008 Springer-Verlag Berlin Heidelberg.

  • 5.
    Bordag, Ljudmila A.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Pricing options in illiquid markets: optimal systems, symmetry reductions and exact solutions2010Inngår i: Lobachevskii Journal of Mathematics, ISSN 1995-0802, E-ISSN 1818-9962, Vol. 31, nr 2, s. 90-99Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study a class of nonlinear pricing models which involves the feedback effect from the dynamic hedging strategies on the price of asset introduced by  Sircar and Papanicolaou. We are first to study the case of a nonlinear demand function involved in the model. Using a Lie group analysis we investigate the symmetry properties of these nonlinear diffusion equations. We provide the optimal systems of subalgebras and the complete set of non-equivalent reductions of studied PDEs to ODEs. In most cases we obtain families of exact solutions or derive particular solutions to the equations.

  • 6.
    Bordag, Ljudmila A.
    Högskolan i Halmstad, Akademin för informationsteknologi, Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Study of the risk-adjusted pricing methodology model with methods of geometrical analysis2011Inngår i: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 83, nr 4-6, s. 333-345Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Families of exact solutions are found to a nonlinear modification of the Black-Scholes equation. This risk-adjusted pricing methodology model (RAPM) incorporates both transaction costs and the risk from a volatile portfolio. Using the Lie group analysis we obtain the Lie algebra admitted by the RAPM equation. It gives us the possibility to describe an optimal system of subalgebras and the corresponding set of invariant solutions to the model. In this way we can describe the complete set of possible reductions of the nonlinear RAPM model. Reductions are given in the form of different second order ordinary differential equations. In all cases we provide exact solutions to these equations in an explicit or parametric form. Each of these solutions contains a reasonable set of parameters which allows one to approximate a wide class of boundary conditions. We discuss the properties of these reductions and the corresponding invariant solutions.

  • 7.
    Bordag, Ljudmila A.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Symmetry reductions and exact solutions for nonlinear diffusion equations2009Inngår i: International Journal of Modern Physics A, ISSN 0217-751X, E-ISSN 1793-656X, Vol. 24, nr 8/9, s. 1713-1716Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The symmetry properties of nonlinear diffusion equations are studied using a Lie group analysis. Reductions and families of exact solutions are found for some of these equations.

    © 2009 World Scientific Publishing Company.

  • 8.
    Bordag, Ljudmila A.
    et al.
    Högskolan i Halmstad, Akademin för informationsteknologi, Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Chmakova, A. Y.
    Fakultät Mathematik, Naturwissenschaften und Informatik, Brandenburgische Technische Universität Cottbus, Cottbus, Germany.
    Explicit solutions for a nonlinear model of financial derivatives2007Inngår i: International Journal of Theoretical and Applied Finance, ISSN 0219-0249, Vol. 10, nr 1, s. 1-21Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Families of explicit solutions are found to a nonlinear Black-Scholes equation which incorporates the feedback-effect of a large trader in case of market illiquidity. The typical solution of these families will have a payoff which approximates a strangle. These solutions were used to test numerical schemes for solving a nonlinear Black-Scholes equation. © World Scientific Publishing Company.

  • 9.
    Bordag, Ljudmila A.
    et al.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Frey, Rüdiger
    Leipzig University, Department of Mathematics.
    Pricing options in illiquid markets: symmetry reductions and exact solutions2008Inngår i: Nonlinear Models in Mathematical Finance: New Research Trends in Option Pricing / [ed] Matthias Ehrhardt, New York: Nova Science Publishers, Inc., 2008, s. 103-130Kapittel i bok, del av antologi (Annet vitenskapelig)
    Abstract [en]

    The present paper is concerned with nonlinear Black Scholes equations arising in certain option pricing models with a large trader and/or transaction costs. In the first part we give an overview of existing option pricing models with frictions. While the financial setup differs between models, it turns out that in many of these models derivative prices can be characterized by fully nonlinear versions of the standard parabolic Black-ScholesPDE. In the second part of the paper we study a typical nonlinear Black-Scholes equation using methods from Lie group analysis. The equation possesses a rich symmetry group. By introducing invariant variables,  invariant solutions can therefore be characterized in terms of solutions to ordinary differential equations. Finally we discuss properties and applications of these solutions.

  • 10.
    Bordag, Ljudmila A.
    et al.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Matveev, Sergey K.
    St. Petersburg State University.
    Erste  Berechnungen der Druckfluidströmung2008Rapport (Annet vitenskapelig)
  • 11.
    Bordag, Ljudmila A.
    et al.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Mikaelyan, Anna
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Models of self-financing hedging strategies in illiquid markets: Symmetry reductions and exact solutions2011Inngår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 96, nr 1-3, s. 191-207Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the general model of self-financing trading strategies inilliquid markets introduced by Schoenbucher and Wilmott, 2000.A hedging strategy in the framework of this model satisfies anonlinear partial differential equation (PDE) which contains somefunction g(alpha). This function is deep connected to anutility function.

    We describe the Lie symmetry algebra of this PDE and provide acomplete set of reductions of the PDE to ordinary differentialequations (ODEs). In addition we are able to describe all types offunctions g(alpha) for which the PDE admits an extended Liegroup. Two of three special type functions lead to modelsintroduced before by different authors, one is new. We clarify theconnection between these three special models and the generalmodel for trading strategies in illiquid markets. We study withthe Lie group analysis the new special case of the PDE describingthe self-financing strategies. In both, the general model and thenew special model, we provide the optimal systems of subalgebrasand study the complete set of reductions of the PDEs to differentODEs. In all cases we are able to provide explicit solutions tothe new special model. In one of the cases the solutions describepower derivative products.

  • 12.
    Bordag, Michael
    et al.
    Univ Leipzig, Vor Hospitaltore 1, D-04103 Leipzig, Germany..
    Nikolaev, Vladimir
    Högskolan i Halmstad, Akademin för informationsteknologi, Halmstad Embedded and Intelligent Systems Research (EIS).
    Analytic corrections to the electromagnetic casimir interaction between a sphere and a plate at shortdistances2010Inngår i: International Journal of Modern Physics A, ISSN 0217-751X, E-ISSN 1793-656X, Vol. 25, nr 11, s. 2171-2176Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    For the vacuum interaction of a sphere in front of a plane, both obeying conductor boundary conditions, we consider the approximation of small separation. We derive the next-to-leading order of the asymptotic expansion in the separation-to-radius ratio epsilon. This correction is of order epsilon. In opposite to the scalar cases it contains also contributions proportional to logarithms in first and second order, epsilon In epsilon and e(ln epsilon)(2). We compare this result with the available findings of numerical and experimental approaches.

  • 13.
    Burnos, Sergey
    et al.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE). Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Ngow, ChaSing
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE). Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    SVI estimation of the implied volatility by Kalman filter.2010Independent thesis Advanced level (degree of Master (One Year)), 15 poäng / 22,5 hpOppgave
    Abstract [en]

    To understand and model the dynamics of the implied volatility smile is essential for trading, pricing and risk management portfolio. We suggest a  linear Kalman filter for updating of the Stochastic Volatility Inspired (SVI) model of the volatility. From a risk management perspective we generate the 1-day ahead forecast of profit and loss (P\&L) of option portfolios. We compare the estimation of the implied volatility using the SVI model with the cubic polynomial model. We find that the SVI Kalman filter has outperformed the  others.

  • 14.
    Dremkova, Ekaterina
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE).
    A high order compact method for nonlinear Black-Scholes option pricing equations with transaction costs2009Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
    Abstract [en]

    In this work we consider the nonlinear case of Black-Scholes equation and apply it to American options. Also, method of Liao and Khaliq of high order was applied to nonlinear Black-Scholes equation in case of American options. Here, we use this method oh fourth order in time and space to raise American option price accuracy.

  • 15.
    Duracz, Adam
    et al.
    Högskolan i Halmstad, Akademin för informationsteknologi, Halmstad Embedded and Intelligent Systems Research (EIS), Centrum för forskning om inbyggda system (CERES).
    Bartha, Ferenc Ágoston
    Rice University, Houston, TX, USA.
    Taha, Walid
    Högskolan i Halmstad, Akademin för informationsteknologi, Halmstad Embedded and Intelligent Systems Research (EIS), Centrum för forskning om inbyggda system (CERES). Rice University, Houston, TX, USA.
    Accurate Rigorous Simulation Should be Possible for Good Designs2016Inngår i: Proceedings of the 2016 International Workshop on Symbolic and Numerical Methods for Reachability Analysis (SNR) / [ed] Erika Ábrahám & Sergiy Bogomolov, Piscataway, NJ: IEEE conference proceedings, 2016, artikkel-id 7479376Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The development of Cyber-Physical Systems benefits from better methods and tools to support the simulation and verification of hybrid (continuous/discrete) models. Acumen is an open source testbed for exploring the design space of what rigorous-but-practical next-generation tools can deliver to developers. Central to Acumen is the notion of rigorous simulation. Like verification tools, rigorous simulation is intended to provide guarantees about the behavior of the system. Like traditional simulation tools, it is intended to be intuitive, practical, and scalable. Whether these two goals can be achieved simultaneously is an important, long-term challenge.

    This paper proposes a design principle that can play an important role in meeting this challenge. The principle addresses the criticism that accumulating numerical errors is a serious impediment to practical rigorous simulation. It is inspired by a twofold insight: one relating to the nature of systems engineered in the real world, and the other relating to how numerical errors in the simulation of a model can be recast as errors in the state or parameters of the model in the simulation. We present a suite of small, concrete benchmarks that can be used to assess the extent to which a rigorous simulator upholds the proposed principle. We also report on which benchmarks Acumen's current rigorous simulator already succeeds and which ones remain challenging.

  • 16.
    Dzharayan, Gayk
    et al.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Voronova, Elena
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Pricing of exotic options under the Kou model by using the Laplace transform2011Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
    Abstract [en]

    In this thesis we present the Laplace transform method of option pricing and it's realization, also compare it with another methods. We consider vanilla and exotic options, but more attention we pay to the two-asset correlation options. We chose the one of the modifications of Black-Scholes model, the Kou double exponential jump-diffusion model with the double exponential distribution of jumps, as model of the underlying stock prices development. The computations was done by the Laplace transform and it's inversion by the Euler method. We will present in details proof of finding Laplace transforms of put and call two-asset correlation options, the calculations of the moment generation function of the jump-diffusion by Levy-Khintchine formulae in cases without jumps and with independent jumps, and direct calculation of the risk-neutral expectation by solving double integral. Our work also contains the programme code for two-asset correlation call and put options. We will show the realization of our programme in the real data. As a result we see how our model complies on the NASDAQ OMX Stock-holm Market, considering the two-asset correlation options on three cases by stock prices of Handelsbanken, Ericsson and index OMXS30.

  • 17.
    Emamizadeh, B.
    et al.
    School of Mathematical Sciences, The University of Nottingham Ningbo, China.
    Farjudian, Amin
    Högskolan i Halmstad, Akademin för informationsteknologi, Halmstad Embedded and Intelligent Systems Research (EIS), Centrum för forskning om inbyggda system (CERES).
    Liu, Y.
    Beijing International Center for Mathematical Research, Peking University, China.
    Optimal harvesting strategy based on rearrangements of functions2018Inngår i: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 320, s. 677-690Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the problem of optimal harvesting of a marine species in a bounded domain, with the aim of minimizing harm to the species, under the general assumption that the fishing boats have different capacities. This is a generalization of a result of Kurata and Shi, in which the boats were assumed to have the same maximum harvesting capacity. For this generalization, we need a completely different approach. As such, we use the theory of rearrangements of functions. We prove existence of solutions, and obtain an optimality condition which indicates that the more aggressive harvesting must be pushed toward the boundary of the domain. Furthermore, we prove that radial and Steiner symmetries of the domain are preserved by the solutions. We will also devise an algorithm for numerical solution of the problem, and present the results of some numerical experiments. © 2017 Elsevier Inc.

  • 18.
    Emamizadeh, Behrouz
    et al.
    The University of Nottingham Ningbo, Ningbo, China.
    Farjudian, Amin
    Högskolan i Halmstad, Akademin för informationsteknologi, Halmstad Embedded and Intelligent Systems Research (EIS), Centrum för forskning om inbyggda system (CERES).
    Mikayelyan, Hayk
    The University of Nottingham Ningbo, Ningbo, China.
    An Elliptic Optimal Control Problem and its Two Relaxations2017Inngår i: Journal of Optimization Theory and Applications, ISSN 0022-3239, E-ISSN 1573-2878, Vol. 172, nr 2, s. 455-465Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this note, we consider a control theory problem involving a strictly convex energy functional, which is not Gâteaux differentiable. The functional came up in the study of a shape optimization problem, and here we focus on the minimization of this functional. We relax the problem in two different ways and show that the relaxed variants can be solved by applying some recent results on two-phase obstacle-like problems of free boundary type. We derive an important qualitative property of the solutions, i.e., we prove that the minimizers are three-valued, a result which significantly reduces the search space for the relevant numerical algorithms. © 2016, Springer Science+Business Media New York.

  • 19.
    Erling, Fredrik
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE).
    Static CFD analysis of a novel valve design for internal combustion engines2011Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
    Abstract [en]

    In this work CFD was used to simulate the flow through a novel valve design for internal combustion engines. CFD is numerical method for simulating the behaviour of systems involving flow processes. A FEM was used for solving the equations.

    Literature on the topic was studied to gain an understanding of the performance limiters on the Internal combustion engine. This understanding was used to set up models that better would mimic physical phenomena compared to previous studies. The models gave plausible results as to fluid velocities and in-cylinder flow patterns.

    Comsol Multiphysics 4.1 was used for the computations.

  • 20.
    Etbaeitabari, Amir
    et al.
    Högskolan i Halmstad, Akademin för ekonomi, teknik och naturvetenskap.
    Barakat, M.
    Univ Denver, Denver, CO USA..
    Imani, A. A.
    Iran Islamic Azad Univ, Babol Branch, Babol Sar, Iran..
    Domairry, G.
    Univ Mazandaran, Dept Mech Engn, Babol Sar, Iran..
    Jalili, P.
    Islamic Azad Univ, Dept Mech Engn, Takestan Branch, Takestan, Iran..
    An analytical heat transfer assessment and modeling in a natural convection between two infinite vertical parallel flat plates2013Inngår i: Journal of Molecular Liquids, ISSN 0167-7322, E-ISSN 1873-3166, Vol. 188, s. 252-257Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Heat transfer by natural convection occurs in many physical problems and engineering applications such as geo-thermal systems, heat exchangers, petroleum reservoirs and nuclear waste repositories. These problems and phenomena are modeled by ordinary or partial differential equations. In most cases, experimental solutions cannot be applied to these problems, so these equations should be solved using special techniques. Recently, much attention has been devoted to these methods to construct analytic solutions; such as the perturbation method. Perturbation techniques are dependent upon small parameter. Thus, it is worthwhile developing a new technique independent of small parameter. The Reconstruction of Variational Iteration Method technique is a powerful and convenient algorithm in finding the solutions for the equations. While this method is capable of reducing the size of calculation, it overcomes the difficulty of the perturbation technique or Adomian polynomials by applying Laplace Transform. In this paper an analysis has been performed to study the natural convection of a non-Newtonian fluid between two infinite parallel vertical flat plates and the effects of the non-Newtonian nature of fluid on the heat transfer are studied. In order to compare with exact solution, velocity and temperature profiles are shown graphically. The obtained results are valid with significant accuracy. (C) 2013 Elsevier B.V. All rights reserved.

  • 21.
    Fang, Fang
    et al.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE).
    Mehrdad, Dinkoo
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE).
    Wave Energy of an Antenna in Matlab2011Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
    Abstract [en]

     In the modern world, because of increasing oil prices and the need to control greenhouse gas emission, a new interest in the production of electric cars is coming about.

    One of the products is a charging point for electric cars, at which electric cars can be recharged by a plug in cable. Usually people are required to pay for the electricity after recharging the electric cars. Today, the payment is handled by using SMS or through the parking system. There is now an opportunity, in cooperation with AES (the company with which we are working), to equip the pole with GPRS, and this requires development and maintenance of the antenna. The project will include data analysis of the problem, measurements and calculations.

    In this work, we are computing energy flow of the wave due to the location of the antenna inside the box. We need to do four steps. First, we take a set of points (determined by the computational mesh) that have the same distance from the antenna in the domain. Second, we calculate the angles between the ground and the points in the set. Third, we do an angle-energy plot, to analyse which angle can give the maximum energy. And last, we need to compare the maximum energy value of different position of the antenna.

    We are going to solve the problem in Matlab, based on the Maxwell equation and the Helmholtz equation, which is not time-dependent.

  • 22.
    Gao, Zhiyuan
    et al.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (CAMP).
    Qi, Likai
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (CAMP).
    Predicting Stock Price Index2010Independent thesis Advanced level (degree of Master (One Year)), 15 poäng / 22,5 hpOppgave
    Abstract [en]

    This study is based on three models, Markov model, Hidden Markov model and the Radial basis function neural network. A number of work has been done before about application of these three models to the stock market. Though, individual researchers have developed their own techniques to design and test the Radial basis function neural network. This paper aims to show the different ways and precision of applying these three models to predict price processes of the stock market. By comparing the same group of data, authors get different results. Based on Markov model, authors find a tendency of stock market in future and, the Hidden Markov model behaves better in the financial market. When the fluctuation of the stock price index is not drastic, the Radial basis function neural network has a nice prediction.

  • 23.
    Guo, Matilda
    et al.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE). Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Lapenkova, Maria
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE). Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Numerical Methods for Pricing Swing Options in the Electricity Market2010Independent thesis Advanced level (degree of Master (One Year)), 15 poäng / 22,5 hpOppgave
    Abstract [en]

    Since the liberalisation of the energy market in Europe in the early 1990s, much opportunity to trade electricity as a commodity has arisen. One significant consequence of this movement is that market prices have become more volatile instead of its tradition constant rate of supply. Spot price markets have also been introduced, affecting the demand of electricity as companies now have the option to not only produce their own supply but also purchase this commodity from the market. Following the liberalisation of the energy market, hence creating a greater demand for trading of electricity and other types of energy, various types of options related to the sales, storage and transmission of electricity have consequently been introduced.

    Particularly, swing options are popular in the electricity market. As we know, swing-type derivatives are given in various forms and are mainly traded as over-the-counter (OTC) contracts at energy exchanges. These options offer flexibility with respect to timing and quantity.

    Traditionally, the Geometric Brownian Motion (GBM) model is a very popular and standard approach for modelling the risk neutral price dynamics of underlyings. However, a limitation of this model is that it has very few degrees of freedom, as it does not capture the complex behaviour of electricity prices. In short the GBM model is inefficient in the pricing of options involving electricity. Other models have subsequently been used to bridge this inadequacy, e.g. spot price models, futures price models, etc.

    To model risk-neutral commodity prices, there are basically two different methodologies, namely spot and futures or so-called term structure models. As swing options are usually written on spot prices, by which we mean the current price at which a particular commodity can be bought or sold at a specified time and place, it is important for us to examine these models in order to more accurately inculcate their effect on the pricing of swing options.

    Monte Carlo simulation is also a widely used approach for the pricing of swing options in the electricity market. Theoretically, Monte Carlo valuation relies on risk neutral valuation and the technique used is to simulate as many (random) price paths of the underlying(s) as possible, and then to average the calculated payoff for each path, discounted to today's prices, giving the value of the desired derivative. Monte Carlo methods are particularly useful in the valuation of derivatives with multiple sources of uncertainty or complicated features, like our electricity swing options in question. However, they are generally too slow to be considered a competitive form of valuation, if any analytical techniques of valuation exist. In other words, the Monte Carlo approach is, in a sense, a method of last resort.

    In this thesis, we aim to examine a numerical method involved in the pricing of swing options in the electricity market. We will consider an existing and widely accepted electricity price process model, use the finite volume method to formulate a numerical scheme in order to calibrate the prices of swing options and make a comparison with numerical solutions obtained using the theta-scheme. Further contributions of this thesis include a comparison of results and also a brief discussion of other possible methods.

  • 24.
    Juszczuk, Agnieszka Beata
    et al.
    Högskolan i Halmstad. Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE). Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Tkacheva, Evgeniya
    Högskolan i Halmstad. Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE). Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Revision Moment for the Retail Decision-Making System2010Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
    Abstract [en]

    In this work we address to the problems of the loan origination decision-making systems. In accordance with the basic principles of the loan origination process we considered the main rules of a clients parameters estimation, a change-point problem for the given data and a disorder moment detection problem for the real-time observations. In the first part of the work the main principles of the parameters estimation are given. Also the change-point problem is considered for the given sample in the discrete and continuous time with using the Maximum likelihood method. In the second part of the work the disorder moment detection problem for the real-time observations is considered as a disorder problem for a non-homogeneous Poisson process. The corresponding optimal stopping problem is reduced to the free-boundary problem with a complete analytical solution for the case when the intensity of defaults increases. Thereafter a scheme of the real time detection of a disorder moment is given.

  • 25.
    Konečný, Michal
    et al.
    Computer Science Group, Aston University, Birmingham, United Kingdom.
    Taha, Walid
    Högskolan i Halmstad, Akademin för informationsteknologi, Halmstad Embedded and Intelligent Systems Research (EIS), Centrum för forskning om inbyggda system (CERES). Department of Computer Science, Rice University, Houston, Texas, USA.
    Bartha, Ferenc Ágoston
    Department of Computer Science, Rice University, Houston, Texas, USA.
    Duracz, Jan
    Högskolan i Halmstad, Akademin för informationsteknologi, Halmstad Embedded and Intelligent Systems Research (EIS), Centrum för forskning om inbyggda system (CERES).
    Duracz, Adam
    Högskolan i Halmstad, Akademin för informationsteknologi, Halmstad Embedded and Intelligent Systems Research (EIS), Centrum för forskning om inbyggda system (CERES).
    Ames, Aaron D.
    Woodruff School of Mechanical Engineering, School of Electrical & Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA.
    Enclosing the behavior of a hybrid automaton up to and beyond a Zeno point2016Inngår i: Nonlinear Analysis: Hybrid Systems, ISSN 1751-570X, E-ISSN 1878-7460, Vol. 20, s. 1-20Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Even simple hybrid automata like the classic bouncing ball can exhibit Zeno behavior. The existence of this type of behavior has so far forced a large class of simulators to either ignore some events or risk looping indefinitely. This in turn forces modelers to either insert ad-hoc restrictions to circumvent Zeno behavior or to abandon hybrid automata. To address this problem, we take a fresh look at event detection and localization. A key insight that emerges from this investigation is that an enclosure for a given time interval can be valid independent of the occurrence of a given event. Such an event can then even occur an unbounded number of times. This insight makes it possible to handle some types of Zeno behavior. If the post-Zeno state is defined explicitly in the given model of the hybrid automaton, the computed enclosure covers the corresponding trajectory that starts from the Zeno point through a restarted evolution. ©2015 The Authors. Published by Elsevier Ltd.

  • 26.
    Konečný, Michal
    et al.
    Aston University, Birmingham, United Kingdom.
    Taha, Walid
    Högskolan i Halmstad, Akademin för informationsteknologi, Halmstad Embedded and Intelligent Systems Research (EIS), Centrum för forskning om inbyggda system (CERES).
    Duracz, Jan
    Högskolan i Halmstad, Akademin för informationsteknologi, Halmstad Embedded and Intelligent Systems Research (EIS), Centrum för forskning om inbyggda system (CERES).
    Duracz, Adam
    Högskolan i Halmstad, Akademin för informationsteknologi, Halmstad Embedded and Intelligent Systems Research (EIS), Centrum för forskning om inbyggda system (CERES).
    Ames, Aaron
    Texas A&M University, College Station, USA.
    Enclosing the Behavior of a Hybrid System up to and Beyond a Zeno Point2013Inngår i: 2013 IEEE 1st International Conference on Cyber-Physical Systems, Networks, and Applications, CPSNA 2013, Piscataway, N.J.: IEEE Press, 2013, s. 120-125Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Even simple hybrid systems like the classic bouncing ball can exhibit Zeno behaviors. The existence of this type ofbehavior has so far forced simulators to either ignore some events or risk looping indefinitely. This in turn forces modelers to either insert ad hoc restrictions to circumvent Zeno behavior or to abandon hybrid modeling. To address this problem, we take a fresh look at event detection and localization. A key insight that emerges from this investigation is that an enclosure for a given time interval can be valid independently of the occurrence of agiven event. Such an event can then even occur an unbounded number of times, thus making it possible to handle certain types of Zeno behavior. © 2013 IEEE.

  • 27.
    Kudla, Jakub
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE). Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Monte Carlo SimulationsMethods in Pricing AmericanType Options2010Independent thesis Advanced level (degree of Master (One Year)), 15 poäng / 22,5 hpOppgave
    Abstract [en]

    The aim of this paper is to present simulation methods for the pricing of American financial instruments. Three methods are presented. Each differs from the others in it's approach to the problem and the method of finding a solution. We illustrate the variety of possible approaches that can be adopted when dealing with this complicated problem. The results of using these algorithms are compared with examples found in literature on the subject. We try to identify the factors that influence price estimators and provide some new results about the properties and distributions of those estimators. We show that even a simple variance reduction technique has a positive effect for these algorithms. The purpose of this paper is to present the effectiveness of a simulation method in pricing American options. This is contrary to the opinion often stated in articles and monographs that the simulation approach is not adequate for the task. We provide an overview and comparison of earlier methods proposed and follow this with an extended discussion. This paper sets the foundations for further research into use of these algorithms for multidimensional problems, where they may offer a substantial advantage over deterministic methods.

  • 28.
    Mezentsev, Anton
    et al.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE).
    Pomelnikov, Anton
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE).
    Valuation of Installment Options 2009Independent thesis Advanced level (professional degree), 15 poäng / 22,5 hpOppgave
  • 29.
    Mezentsev, Anton
    et al.
    Högskolan i Halmstad, Akademin för informationsteknologi, Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Pomelnikov, Anton
    Högskolan i Halmstad, Akademin för informationsteknologi, Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Ehrhardt, Matthias
    University Wuppertal, Wuppertal, Deutschland.
    Efficient Numerical Valuation of Continuous Installment Options2011Inngår i: Advances in Applied Mathematics and Mechanics, ISSN 2070-0733, E-ISSN 2075-1354, Vol. 3, nr 2, s. 141-164Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this work we investigate the novel Kryzhnyi method for the numerical inverse Laplace transformation and apply it to the pricing problem of continuous installment options. We compare the results with the one obtained using other classical methods for the inverse Laplace transformation, like the Euler summation method or the Gaver-Stehfest method.

  • 30.
    Mikaelyan, Anna
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE).
    Analitical study of the Schönbucher-Wilmott model of the feedback effect in illiquid markets2009Independent thesis Advanced level (degree of Master (One Year)), 15 poäng / 22,5 hpOppgave
    Abstract [en]

    This master project is dedicated to the analysis of one of the nancialmarket models in an illiquid market. This is a nonlinear model. Using analytical methods we studied the symmetry properties of theequation which described the given model. We called this equation aSchonbucher-Wilmott equation or the main equation. We have foundinnitesimal generators of the Lie algebra, containing the informationabout the symmetry group admitted by the main equation. We foundthat there could be dierent types of the unknown function g, whichwas located in the main equation, in particular four types which admitsricher symmetry group. According to the type of the function gthe equation was split up into four PDEs with the dierent Lie algebrasin each case. Using the generators we studied the structure ofthe Lie algebras and found optimal systems of subalgebras. Then weused the optimal systems for dierent reductions of the PDE equationsto some ODEs. Obtained ODEs were easier to solve than the correspondingPDE. Thereafter we proceeded to the solution of the desiredSchonbucher-Wilmott equation. In the project we were guided by thepapers of Bank, Baum [1] and Schonbucher, Wilmott [2]. In these twopapers authors introduced distinct approaches of the analysis of thenonlinear model - stochastic and dierential ones. Both approaches leadunder some additional assumptions to the same nonlinear equation - the main equation.

  • 31.
    Moggi, E.
    et al.
    DIBRIS, Genova Univ., v. Dodecaneso 35, Genova, 16146, Italy.
    Farjudian, A.
    University of Nottingham Ningbo, China.
    Duracz, Adam
    Rice University, Houston, TX, United States.
    Taha, Walid
    Högskolan i Halmstad, Akademin för informationsteknologi, Halmstad Embedded and Intelligent Systems Research (EIS), Centrum för forskning om inbyggda system (CERES).
    Safe & robust reachability analysis of hybrid systems2018Inngår i: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 747, s. 75-99Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Hybrid systems—more precisely, their mathematical models—can exhibit behaviors, like Zeno behaviors, that are absent in purely discrete or purely continuous systems. First, we observe that, in this context, the usual definition of reachability—namely, the reflexive and transitive closure of a transition relation—can be unsafe, i.e., it may compute a proper subset of the set of states reachable in finite time from a set of initial states. Therefore, we propose safe reachability, which always computes a superset of the set of reachable states. Second, in safety analysis of hybrid and continuous systems, it is important to ensure that a reachability analysis is also robust w.r.t. small perturbations to the set of initial states and to the system itself, since discrepancies between a system and its mathematical models are unavoidable. We show that, under certain conditions, the best Scott continuous approximation of an analysis A is also its best robust approximation. Finally, we exemplify the gap between the set of reachable states and the supersets computed by safe reachability and its best robust approximation. © 2018 The Authors

  • 32.
    Nadratowska, Natalia Beata
    et al.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE).
    Prochna, Damian
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE).
    Option pricing under the double exponential jump-diffusion model by using the Laplace transform: Application to the Nordic market2010Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
    Abstract [en]

    In this thesis the double exponential jump-diffusion model is considered and the Laplace transform is used as a method for pricing both plain vanilla and path-dependent options. The evolution of the underlying stock prices are assumed to follow a double exponential jump-diffusion model. To invert the Laplace transform, the Euler algorithm is used. The thesis includes the programme code for European options and the application to the real data. The results show how the Kou model performs on the NASDAQ OMX Stockholm Market in the case of the SEB stock.

  • 33.
    Persson, Sandra
    et al.
    Högskolan i Halmstad, Sektionen för lärarutbildning (LUT).
    Lindgren, Terese
    Högskolan i Halmstad, Sektionen för lärarutbildning (LUT).
    Mästare i matematik med Mästerkatten?: - analys av matematikböcker2010Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Trots att läroböcker i matematik har en viktig roll i undervisningen, så finns det inte mycket forskning på hur väl de uppfyller sin uppgift. Rapporter om lärobokens roll i skolan förekommer, dock oftast med en negativ klang. Forskning som vi har uppmärksammat tar upp att läroböckerna styr undervisning. Det nationella provet som utfördes för årskurs 3 2009, visade att eleverna har vissa brister i sina matematikkunskaper. Det står i kursplanen för matematik att det är skolans uppgift att utveckla kunskaper som behövs i matematiken för att eleverna ska kunna fatta välgrundade beslut i valsituationer (Skolverket, 2009-11-28). Med ovanstående i åtanke uppkom denna studie med syfte i att ta reda på hur en matematikbok kan se ut och i vilken grad den kan erbjuda eleverna tillfällen att träna de uppsatta målen som finns för årskurs 3.

     

    Resultatet av föreliggande studie visar att de undersökta matematikböckerna inte motsvarar de krav som finns gällande de uppsatta målen för vad eleverna ska uppnå i matematik, till och med årskurs 3. Matematikböckerna tränar ej alla de utsatta målen för matematik. I vår undersökning delade vi upp uppgifterna i kreativa respektive imitativa resonemang. Imitativa resonemang innebär uppgifter som kräver en inövad metod eller ett memorerat svar och dessa uppgifter fanns det betydligt fler av. Kreativa resonemang kräver en ny sorts lösningsmetod för eleverna och var mycket mindre representerade i de båda matematikböckerna vi undersökt. Tidigare forskning har visat på att kreativa resonemang ger eleverna större förståelse för matematik. Med resultatet från nationella provet i åtanke, visade det sig att inte alla elever hade lyckats ta till sig förståelse för de olika räknesätten. Matematikböckernas uppgifter har i studien delats upp i delar som bygger på målen för matematik i årskurs 3. Utifrån delarna har vi sedan kunnat hitta mönster och dragit slutsatser om matematikböckerna som helhet. De undersökta matematikböckerna utger sig ej för att träna alla målen och det är upp till lärarna att kunna ge förutsättningar så att eleverna når alla målen i slutet på årskurs 3. Böckerna utger sig heller inte för att träna imitativa eller kreativa resonemang.

     

    Vi kan genom denna studie rekommendera lärare att uppmärksamma olika matematikböckers innehåll. De bör undersöka vad böckerna kan erbjuda eleverna, för att eleverna ska kunna ha goda förutsättningar för att bli mästare i matematik.

  • 34.
    Petrova, Liudmila
    et al.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE).
    Ivkina, Liubov
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE).
    Study of the group properties of the Sircar-Papanicolaou model in case of a nonlinear utility function2009Independent thesis Advanced level (degree of Master (One Year)), 15 poäng / 22,5 hpOppgave
    Abstract [en]

    In this paper it is considered the Sircar-Papanicolaou model wich takesinto account a feedback effect of dynamic hedging strategies of pro-gramme traders. Using the Lie group analysis we describe the symmetrygroup of the main equation of the concerned model. We reduce this par-tial differential equation to the ordinary differential equations by usingcorresponding invariants of the subgroups of the main symmetry group.

  • 35.
    Prostakova, Irina
    et al.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Tazov, Alexander
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Energy Derivatives Pricing2011Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
    Abstract [en]

    In this paper we examine energy derivatives pricing. The previous studies considered the same source of uncertainty for the spot and the futures prices. We investigate the problem of futures pricing with two independent sources of risk. In general the structure of the oil and gas futures markets is closely related to some stock indices. Therefore, we develop a model for the futures market and compound derivatives with pricing in accordance with the correspondent index. We derive a framework for energy derivatives pricing, compute the price of the European call option on futures and corresponding hedging strategy. We calculate the price of the European call option adjusted for an index level, study the American put option on futures and corresponding hedging strategies.

  • 36.
    Reducha, Wojciech
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (CAMP).
    Parameter Estimation of the Pareto-Beta Jump-Diffusion Model in Times of Catastrophe Crisis2011Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
    Abstract [en]

    Jump diffusion models are being used more and more often in financial applications. Consisting of a Brownian motion (with drift) and a jump component, such models have a number of parameters that have to be set at some level. Maximum Likelihood Estimation (MLE) turns out to be suitable for this task, however it is computationally demanding. For a complicated likelihood function it is seldom possible to find derivatives. The global maximum of a likelihood function defined for a jump diffusion model can however, be obtained by numerical methods. I chose to use the Bound Optimization BY Quadratic Approximation (BOBYQA) method which happened to be effective in this case. However, results of Maximum Likelihood Estimation (MLE) proved to be hard to interpret.

  • 37.
    Shcherbakov, Dmitry
    et al.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE). Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Szwaczkiewicz, Sylwia
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE). Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Exponential Fitting, Finite Volume and Box Methods in Option Pricing.2010Independent thesis Advanced level (degree of Master (One Year)), 15 poäng / 22,5 hpOppgave
    Abstract [en]

    In this thesis we focus mainly on special finite differences and finite volume methods and apply them to the pricing of barrier options.The structure of this work is the following: in Chapter 1 we introduce the definitions of options and illustrate some properties of vanilla European options and exotic options.Chapter 2 describes a classical model used in the financial world, the  Black-Scholes model. We derive theBlack-Scholes formula and show how stochastic differential equations model financial instruments prices.The aim of this chapter is also to present the initial boundary value problem and the maximum principle.We discuss boundary conditions such as: the first boundary value problem, also called  Dirichlet problem that occur in pricing ofbarrier options and European options. Some kinds of put options lead to the study of a second boundary value problem (Neumann, Robin problem),while the Cauchy problem is associated with one-factor European and American options.Chapter 3 is about finite differences methods such as theta, explicit, implicit and Crank-Nicolson method, which are used forsolving partial differential equations.The exponentially fitted scheme is presented in Chapter 4. It is one of the new classesof a robust difference scheme that is stable, has good convergence and does not produce spurious oscillations.The stability is also advantage of the box method that is presented in Chapter 5.In the beginning of the Chapter 6 we illustrate barrier options and then we consider a novel finite volume discretization for apricing the above options.Chapter 7 describes discretization of the Black-Scholes equation by the fitted finite volume scheme. In  Chapter 8 we present and describe numerical results obtained by using  the finite difference methods illustrated in the previous chapters.

  • 38.
    Shcherbakova, Evgenia
    et al.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE). Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Gogoleva, Olga
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE). Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    On-line change-point detection procedures for Initial Public Offerings2010Independent thesis Advanced level (degree of Master (One Year)), 15 poäng / 22,5 hpOppgave
    Abstract [en]

     

    In this thesis we investigate the case of monitoring of stocks havingjust been introduced for public trading on the nancial market. Theempirical distribution of the change-point for 20 assets for 60 days was calculated to check the support for the assumption that the priceinitially drop or rise to some steady level.The price process X = {Xt : t in Z} is assumed to be an AR(1) process with a shift in the mean value from a slope to a constant. The Shiryaev-Roberts, Shewhart, EWMA, Likelihood ratio and CUSUM proceduresfor detecting a change-point in such a process are derived. The expecteddelay of the motivated alarm according to these methods is achievedunder the assumptions of a Poisson, uniform, binomial and geometric distributed 

    by means of simulations.

     

      

     

  • 39.
    Somnicki, Emil
    et al.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE).
    Ostrowski, Krzysztof
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE).
    How useful are intraday data in Risk Management?: An application of high frequency stock returns of three Nordic Banks to the VaR and ES calculation2010Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
    Abstract [en]

    The work is focused on the Value at Risk and the Expected Shortfallcalculation. We assume the returns to be based on two pillars - the white noise and the stochastic volatility. We assume that the white noise follows the NIG distribution and the volatility is modeled using the nGARCH, NIG-GARCH, tGARCH and the non-parametric method. We apply the models into the stocks of three Banks of the Nordic market. We consider the daily and the intraday returns with the frequencies 5, 10, 20 and 30 minutes. We calculate the one step ahead VaR and ES for the daily and the intraday data. We use the Kupiec test and the Markov test to assess the correctness of the models. We also provide a new concept of improving the daily VaR calculation by using the high frequency returns. The results show that the intraday data can be used to the one step ahead VaR and the ES calculation. The comparison of the VaR for the end of the following trading day calculated on the basis of the daily returns and the one computed using the high frequency returns shows that using the intraday data can improve the VaR outcomes.

  • 40.
    Takac, Michal
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Operator Splitting Techniques for American Type of Floating Strike Asian Option2011Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
    Abstract [en]

    In this thesis we investigate Asian oating strike options. We particu-larly focus on options with early exercise - American options. This typeof options are very lucrative to the end-users of commodities or ener-gies who are tend to be exposed to the average prices over time. Asianoptions are also very popular with corporations, who have ongoing cur-rency exposures. The main idea of the pricing is to examine the freeboundary position on which the value of the option is depending. Wefocus on developing a ecient numerical algorithm for this boundary.In the rst Chapter we give an informative description of the nancialderivatives including Asian options. The second Chapter is devoted tothe analytical derivation of the corresponding partial dierential equa-tion coming from the original Black - Scholes equation. The problemis simplied using transformation methods and dimension reduction. Inthe third and fourth Chapter we describe important numerical methodsand discretize the problem. We use the rst order Lie splitting and thesecond order Strang splitting. Finally, in the fth Chapter we makenumerical experiments with the free boundary and compare the resultwith other known methods.

  • 41.
    Tkachev, Ilya
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE).
    Hedging strategy for an option on commodity market2010Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
    Abstract [en]

    In this work we consider the methods of pricing and hedging an option on the forward commodity market described by the multi-factor diffusion model. In the previous research there were presented explicit valuation formulas for standard European type options and simulation schemes for other types of options. However, hedging strategies were not developed in the available literature. Extending known results this work gives analytical formulas for the price of American, Asian and general European options. Moreover, for all these options hedging strategies are presented. Using these results the dynamics of the portfolio composed of options on futures with different maturities is studied on a commodity market.

  • 42.
    Uhliarik, Marek
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE). Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Operator Splitting Methods and Artificial Boundary Conditions for a nonlinear       Black-Scholes equation2010Independent thesis Advanced level (degree of Master (One Year)), 15 poäng / 22,5 hpOppgave
    Abstract [en]

    There are some nonlinear models for pricing financial derivatives which can improve the linear Black-Scholes model introduced by Black, Scholes and Merton. In these models volatility is not constant anymore, but depends on some extra variables. It can be, for example, transaction costs, a risk from a portfolio, preferences of a large trader, etc. In this thesis we focus on these models.

    In the first chapter we introduce some important theory of financial derivatives. The second chapter is devoted to the volatility models. We derive three models concerning transaction costs (RAPM, Leland's  and Barles-Soner's model) and Frey's model which assumes a large (dominant) trader on the market. In the third and in the forth chapter we derive portfolio and make numerical experiments with a free boundary. We use the first order additive and the second order Strang splitting methods. We also use approximations of Barles-Soner's model using the identity function and introduce an approximation with the logarithm function of Barles-Soner's model. These models we finally compare with models where the volatility includes constant transaction costs.

  • 43.
    Valivarthi, Mohan Varma
    et al.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE).
    Muthyala, Hema Chandra Babu
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE).
    A Finite Element Time Relaxation Method2012Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
    Abstract [en]

    In our project we discuss a finite element time-relaxation method for high Reynolds number flows. The key idea consists of using local projections on polynomials defined on macro element of each pair of two elements sharing a face. We give the formulation for the scalar convection–diffusion equation and a numerical illustration.

  • 44.
    Vasilieva, Olesya
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (CAMP).
    A new method of pricing multi-options using Mellin transforms and Integral equations2009Independent thesis Advanced level (degree of Master (One Year)), 40 poäng / 60 hpOppgave
    Abstract [en]

    In this thesis a new method for the option pricing will be introduced with

    the help of the Mellin transforms. Firstly, the Mellin transform techniques for

    options on a single underlying stock is presented. After that basket options

    will be considered. Finally, an improvement of existing numerical results

    applied to Mellin transforms for 1-basket and 2-basket American Put Option

    will be discussed concisely. Our approach does not require either variable

    transformations or solving diusion equations.

  • 45.
    wu, yunxian
    et al.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE).
    wang, yiyun
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE).
    A Drucker-Prager model for elastic contact with friction2011Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
    Abstract [en]

    In mumerical contact simulations with friction, the simple Coloumb law is usually employed. Standard plasticity models are difficult to use since the balance enforced on the contact surface typically only involves balance of traction vectors, and does not use the full stress tensor on the interface. In this work we describe an approach that allows for the use of the stress tensor, thus opening up the possibility of using more advanced plasticity models. We exemplify this approach by implementing the Drucker-Prager pressure sensitive plasticity model.

  • 46.
    Ye, Hui
    et al.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE). Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Ellanskaya, Anastasia
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE). Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Arbitrage-free market models for interest rate options and future options: the multi-strike case2010Independent thesis Advanced level (degree of Master (One Year)), 15 poäng / 22,5 hpOppgave
    Abstract [en]

    This work mainly studies modeling and existence issues for martingale models of option markets with one stock and a collection of European call options for one fixed maturity and infinetely many strikes. In particular, we study Dupire's and Schweizer-Wissel's models, especially the latter one. These two types of models have two completely different pricing approachs, one of which is martingale approach (in Dupire's model), and other one is a market approach (in Schweizer-Wissel's model). After arguing that Dupire's model suffers from the several lacks comparing to Schweizer-Wissel's model, we extend the latter one to get the variations for the case of options on interest rate indexes and futures options. Our models are based on the newly introduced definitions of local implied volatilities and a price level proposed by Schweizer and Wissel. We get explicit expressions of option prices as functions of the local implied volatilities and the price levels in our variations of models. Afterwards, the absence of the dynamic arbitrage in the market for such models can be described in terms of the drift restrictions on the models' coefficients. Finally we demonstrate the application of such models by a simple example of an investment portfolio to show how Schweizer-Wissel's model works generally.

  • 47.
    Zhelezov, Dmitry
    et al.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Yamshchikov, Ivan
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Liquidity and optimal consumption with random income2011Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
    Abstract [en]

    In the first part of our work we focus on the model of the optimal consumption with a random income. We provide the three dimensional equation for this model, demonstrate the reduction to the two dimensional case and provide for two different utility functions the full point-symmetries' analysis of the equations. We also demonstrate that for the logarithmic utility there exists a unique and smooth viscosity solution the existence of which as far as we know was never demonstrated before.

    In the second part of our work we develop the concept of the empirical liquidity measure. We provide the retrospective view of the works on this issue, discuss the proposed definitions and develop our own empirical measure based on the intuitive mathematical model and comprising several features of the definitions that existed before. Then we verify the measure provided on the real data from the market and demonstrate the advantages of the proposed value for measuring the illiquidity.

1 - 47 of 47
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