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  • 1.
    Bordag, Ljudmila A.
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), MPE-lab.
    Pricing options in illiquid markets: optimal systems, symmetry reductions and exact solutions2010In: Lobachevskii Journal of Mathematics, ISSN 1995-0802, E-ISSN 1818-9962, Vol. 31, no 2, p. 90-99Article in journal (Refereed)
    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.

  • 2.
    Bordag, Ljudmila A.
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), MPE-lab.
    Symmetry reductions and exact solutions for nonlinear diffusion equations2009In: International Journal of Modern Physics A, ISSN 0217-751X, E-ISSN 1793-656X, Vol. 24, no 8/9, p. 1713-1716Article in journal (Refereed)
    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.

  • 3.
    Bordag, Michael
    et al.
    Univ Leipzig, Vor Hospitaltore 1, D-04103 Leipzig, Germany..
    Nikolaev, Vladimir
    Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS).
    Analytic corrections to the electromagnetic casimir interaction between a sphere and a plate at shortdistances2010In: International Journal of Modern Physics A, ISSN 0217-751X, E-ISSN 1793-656X, Vol. 25, no 11, p. 2171-2176Article in journal (Refereed)
    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.

  • 4.
    Bukina, Elena
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), MPE-lab.
    Efficient Numerical Solution of PIDEs in Option Pricing2011Independent thesis Advanced level (degree of Master (One Year)), 15 credits / 22,5 HE creditsStudent thesis
  • 5.
    Demin, Mikhail
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), MPE-lab.
    Finite Volume Methods for Option Pricing2011Independent thesis Advanced level (degree of Master (One Year)), 15 credits / 22,5 HE creditsStudent thesis
  • 6. Duracz, Jan
    et al.
    Farjudian, Amin
    University of Nottingham Ningbo China, Ningbo, China.
    Konečný, Michal
    Aston University, Birmingham, United Kingdom.
    Taha, Walid
    Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS), Centre for Research on Embedded Systems (CERES). Rice University, Houston, Texas, USA.
    Function Interval Arithmetic2014In: Mathematical software -- ICMS 2014: 4th International Congress, Seoul, South Korea, August 5-9, 2014. Proceedings / [ed] Hoon Hong & Chee Yap, Berlin, Heidelberg: Springer, 2014, p. 677-684Conference paper (Refereed)
    Abstract [en]

    We propose an arithmetic of function intervals as a basis for convenient rigorous numerical computation. Function intervals can be used as mathematical objects in their own right or as enclosures of functions over the reals. We present two areas of application of function interval arithmetic and associated software that implements the arithmetic: (1) Validated ordinary differential equation solving using the AERN library and within the Acumen hybrid system modeling tool. (2) Numerical theorem proving using the PolyPaver prover. © 2014 Springer-Verlag.

  • 7.
    Emamizadeh, B.
    et al.
    School of Mathematical Sciences, The University of Nottingham Ningbo, China.
    Farjudian, Amin
    Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS), Centre for Research on Embedded Systems (CERES).
    Liu, Y.
    Beijing International Center for Mathematical Research, Peking University, China.
    Optimal harvesting strategy based on rearrangements of functions2018In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 320, p. 677-690Article in journal (Refereed)
    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.

  • 8.
    Emamizadeh, Behrouz
    et al.
    School of Mathematical Sciences, The University of Nottingham Ningbo, China.
    Farjudian, Amin
    Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS), Centre for Research on Embedded Systems (CERES).
    Existence and uniqueness of solutions for nonlocal p-Laplacian problems2016In: Electronic Journal of Differential Equations, ISSN 1550-6150, E-ISSN 1072-6691, Vol. 2016, no 274, p. 1-9Article in journal (Refereed)
    Abstract [en]

    We study the existence and uniqueness of positive solutions to a class of nonlocal boundary-value problems involving the p-Laplacian. Our main tools are a variant of the Schaefer's fixed point theorem, an inequality which suitably handles the p-Laplacian operator, and a Sobolev embedding which is applicable to the bounded domain. © 2016 Texas State University.

  • 9.
    Emamizadeh, Behrouz
    et al.
    School of Mathematical Sciences, The University of Nottingham Ningbo, Ningbo, China.
    Farjudian, Amin
    Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS), Centre for Research on Embedded Systems (CERES).
    Zivari-Rezapour, Mohsen
    Department of Mathematics, Faculty of Mathematical Sciences & Computer, Shahid Chamran University, Ahvaz, Iran.
    Optimization Related to Some Nonlocal Problems of Kirchhoff Type2016In: Canadian Journal of Mathematics - Journal Canadien de Mathematiques, ISSN 0008-414X, E-ISSN 1496-2479, Vol. 68, no 3, p. 521-540Article in journal (Refereed)
    Abstract [en]

    In this paper we introduce two rearrangement optimization problems, one being a maximization and the other a minimization problem, related to a nonlocal boundary value problem of Kirchhoff type. Using the theory of rearrangements as developed by G. R. Burton we are able to show that both problems are solvable, and derive the corresponding optimality conditions. These conditions in turn provide information concerning the locations of the optimal solutions. The strict convexity of the energy functional plays a crucial role in both problems. The popular case in which the rearrangement class (i.e., the admissible set) is generated by a characteristic function is also considered. We show that in this case, the maximization problem gives rise to a free boundary problem of obstacle type, which turns out to be unstable. On the other hand, the minimization problem leads to another free boundary problem of obstacle type, which is stable. Some numerical results are included to confirm the theory.

  • 10.
    Etbaeitabari, Amir
    et al.
    Halmstad University, School of Business, Engineering and Science.
    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 plates2013In: Journal of Molecular Liquids, ISSN 0167-7322, E-ISSN 1873-3166, Vol. 188, p. 252-257Article in journal (Refereed)
    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.

  • 11.
    Gustavsson, Martin
    et al.
    Halmstad University, School of Information Technology.
    Frimodig, Viktor
    Halmstad University, School of Information Technology.
    Virtual Prototyping and Physical Validation of an Inverted Pendulum: "Sea-Calf Bot"2015Independent thesis Basic level (university diploma), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    The work is motivated by the goal of linking reality and model, and to see if there is an opportunity to develop an inexpensive educational tool for training in cyber-physical systems.

    This project has investigated the possibilities to build a cheap inverted pendulum with controller and connect this with the modeling language Acumen. Acumen models is used for comparison with the actual prototype.

    To solve these problems has a 3D printer been used to create hardware, Arduino UNO for control and Raspberry Pi for enable communication with Acumen over WLAN.

    The result was a cheap inverted pendulum, which can be built for a cost around 750 SEK. Graphs created in Acumen and from data collected from sensors can be analyzed.

    With a model of the inverted pendulum system, the results show that Acumen can be used in the development of cyber-physical systems. There are differences between model and reality but also similarities.

  • 12.
    Järpe, Eric
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), CAISR - Center for Applied Intelligent Systems Research.
    Räkna med rester: Matematik att tillämpas inom kryptologi2013Book (Other academic)
    Abstract [sv]

    Ämnet kryptologi, dvs. kryptering, dekryptering och kodknäckning ­omfattar såväl matematik, dator­programmering som allmän finurlighet. Denna bok behandlar Caesarkrypto, substitutionskrypto, Vignèrekrypto, RSA-krypto och den bakom­liggande ­matematiken (ekvations­lösning, räkning med exponential­uttryck, resträkning, primtalsteori och rekursion) samt angränsande matematik (såsom kombinatorik, statisti­ska metoder för t.ex. detektering av krypterad kod och beräkning av överföringskvalitet). Boken innehåller även en så pass bred ­genomgång av elementär algebra (mängdlära, logik, trigono­metri, komplexa tal och rekurrensekva­tioner) och analys (funktioner i en variabel, derivata och integraler) att den kan användas vid inledande studier i matematik inom en mängd olika utbildningar. Boken syftar till att ge en introduktion till kryptologisk problem­lösning och visa på de stora synergieffekter som uppnås genom att tillämpa en väl­balanserad ­kombination av grundläggande matematik och elementär programmering inom området. Förhoppningen är också att läsaren, sporrad av de nyvunna insikterna om kryptologi, lockas till vidare kunskapsfördjupning. Boken vänder sig i första hand till blivande IT-forensiker som kan behöva kompetensen att kryptera och knäcka krypton i sin yrkesroll men som inte har en omfattande matematisk förkunskap. Den ­vänder sig även till studenter på landets tekniska högskolor och ­universitet.

  • 13.
    Konečný, Michal
    et al.
    Aston University, Birmingham, United Kingdom.
    Duracz, Jan
    Farjudian, Amin
    University of Nottingham Ningbo China, Ningbo, China.
    Taha, Walid
    Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS), Centre for Research on Embedded Systems (CERES).
    Picard Method for Enclosing ODEs with Uncertain Initial Values2014In: 11th International Conference on Computability and Complexity in Analysis: July 21 - 24, 2014: Proceedings, 2014, p. 41-42Conference paper (Refereed)
  • 14.
    Liu, Yichen
    et al.
    Beijing International Center for Mathematical Research, Peking University, China.
    Emamizadeh, Behrouz
    School of Mathematical Sciences, The University of Nottingham-Ningbo, China.
    Farjudian, Amin
    Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS), Centre for Research on Embedded Systems (CERES).
    Optimization problems with fixed volume constraints and stability results related to rearrangement classes2016In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 443, no 2, p. 1293-1310Article in journal (Refereed)
    Abstract [en]

    The material in this paper has been divided into two main parts. In the first part we describe two optimization problems—one maximization and one minimization—related to a sharp trace inequality that was recently obtained by G. Auchmuty. In both problems the admissible set is the one comprising characteristic functions whose supports have a fixed measure. We prove the maximization to be solvable, whilst the minimization will turn out not to be solvable in general. We will also discuss the case of radial domains. In the second part of the paper, we study approximation and stability results regarding rearrangement optimization problems. First, we show that if a sequence of the generators of rearrangement classes converges, then the corresponding sequence of the optimal solutions will also converge. Second, a stability result regarding the Hausdorff distance between the weak closures of two rearrangement classes is presented. © 2016 Elsevier 

  • 15.
    Mikaelyan, Anna
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE).
    Analitical study of the Schönbucher-Wilmott model of the feedback effect in illiquid markets2009Independent thesis Advanced level (degree of Master (One Year)), 15 credits / 22,5 HE creditsStudent thesis
    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.

  • 16.
    Mironenko, Georgy
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), MPE-lab.
    Problem of hedging of a portfolio with a unique rebalancing moment2012Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    The paper deals with the problem of finding an optimal one-time rebalancing strategy for the Bachelier model, and makes some remarks for the similar problem within Black-Scholes model. The problem is studied on finite time interval under mean-square criterion of optimality. The methods of the paper are based on the results for optimal stopping problem and standard mean-square criterion.

    The solution of the problem, considered in the paper, let us interpret how and - that is more important for us -when investor should rebalance the portfolio, if he wants to hedge it in the best way. 

  • 17.
    Rehurek, Adam
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), MPE-lab.
    Stable Numerical Methods for PDE Models of Asian Options2011Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Asian options are exotic financial derivative products which price must be calculated by numerical evaluation. In this thesis, we study certain ways of solving partial differential equations, which are associated with these derivatives. Since standard numerical techniques for Asian options are often incorrect and impractical, we discuss their variations, which are efficiently applicable for handling frequent numerical instabilities reflected in form of oscillatory solutions. We will show that this crucial problem can be treated and eliminated by adopting flux limiting techniques, which are total variation dimishing.

  • 18.
    Sandquist, Sebastian
    Halmstad University, School of Teacher Education (LUT).
    Det blir mer svart på vitt: En studie om lärares inställning till kursplanoch nationella matematikprov i årskurs 32011Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
  • 19.
    Takac, Michal
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), MPE-lab.
    Operator Splitting Techniques for American Type of Floating Strike Asian Option2011Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
    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.

  • 20.
    Tkachev, Ilya
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE).
    Hedging strategy for an option on commodity market2010Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
    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.

  • 21.
    Zhelezov, Dmitry
    et al.
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), MPE-lab.
    Yamshchikov, Ivan
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), MPE-lab.
    Liquidity and optimal consumption with random income2011Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
    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.

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