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  • 1.
    Belova, Anna
    et al.
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE).
    Shmidt, Tamara
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), MPE-lab.
    Meshfree methods in option pricing2011Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    A meshfree approximation scheme based on the radial basis function methods is presented for the numerical solution of the options pricing model. This thesis deals with the valuation of the European, Barrier, Asian, American options of a single asset and American options of multi assets. The option prices are modeled by the Black-Scholes equation. The θ-method is used to discretize the equation with respect to time. By the next step, the option price is approximated in space with radial basis functions (RBF) with unknown parameters, in particular, we con- sider multiquadric radial basis functions (MQ-RBF). In case of Ameri- can options a penalty method is used, i.e. removing the free boundary is achieved by adding a small and continuous penalty term to the Black- Scholes equation. Finally, a comparison of analytical and finite difference solutions and numerical results from the literature is included.

  • 2.
    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.

  • 3.
    Hierons, Robert M.
    et al.
    Department of Computer Science, Brunel University London, Uxbridge, United Kingdom.
    Mousavi, Mohammad Reza
    Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS), Centre for Research on Embedded Systems (CERES).
    Thomsen, Michael Kirkedal
    Department of Computer Science, University of Copenhagen, Copenhagen, Denmark.
    Turker, Uraz Cengiz
    Computer Engineering, Faculty of Engineering, Gebze Technical University, Kocaeli, Turkey.
    Hardness of deriving invertible sequences from finite state machines2017In: SOFSEM 2017: SOFSEM 2017: Theory and Practice of Computer Science: 43rd International Conference on Current Trends in Theory and Practice of Computer Science Limerick, Ireland, January 16–20, 2017, Proceedings / [ed] Bernhard Steffen, Christel Baier, Mark van den Brand, Johann Eder, Mike Hinchey & Tiziana Margaria, Heidelberg: Springer Berlin/Heidelberg, 2017, p. 147-160Conference paper (Refereed)
    Abstract [en]

    Many test generation algorithms use unique input/output sequences (UIOs) that identify states of the finite state machine specification M. However, it is known that UIO checking the existence of UIO sequences is PSPACE-complete. As a result, some UIO generation algorithms utilise what are called invertible sequences; these allow one to construct additional UIOs once a UIO has been found. We consider three optimisation problems associated with invertible sequences: deciding whether there is a (proper) invertible sequence of length at least K; deciding whether there is a set of invertible sequences for state set S′ that contains at most K input sequences; and deciding whether there is a single input sequence that defines invertible sequences that take state set S″ to state set S′. We prove that the first two problems are NP-complete and the third is PSPACE-complete. These results imply that we should investigate heuristics for these problems. © Springer International Publishing AG 2017.

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