Yazar "Soleymani, Fazlollah" seçeneğine göre listele

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    An optimized Steffensen-type iterative method with memory associated with annuity calculation
    (Springer Heidelberg, 2019) Khdhr, Fuad W.; Soleymani, Fazlollah; Saeed, Rostam K.; Akgul, Ali
    An iteration scheme in the class of Steffensen-type methods is proposed and extended to achieve the optimized speed for methods with memory. In fact, 100% convergence acceleration is obtained in contrast to its version without memory and without any additional functional evaluations. Improvements of the convergence radii by this technique are illustrated by the dynamic of the iterations. Finally, an application of the proposed scheme in computing annuity in finance is furnished.
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    Asset pricing for an affine jump-diffusion model using an FD method of lines on nonuniform meshes
    (Wiley, 2019) Soleymani, Fazlollah; Akgul, Ali
    We present a novel numerical scheme for the valuation of options under a well-known jump-diffusion model. European option pricing for such a case satisfies a 1 + 2 partial integro-differential equation (PIDE) including a double integral term, which is nonlocal. The proposed approach relies on nonuniform meshes with a focus on the discontinuous and degenerate areas of the model and applying quadratically convergent finite difference (FD) discretizations via the method of lines (MOL). A condition for observing the time stability of the fully discretized problem is given. Also, we report results of numerical experiments.
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    EUROPEAN OPTION VALUATION UNDER THE BATES PIDE IN FINANCE: A NUMERICAL IMPLEMENTATION OF THE GAUSSIAN SCHEME
    (Amer Inst Mathematical Sciences-Aims, 2020) Soleymani, Fazlollah; Akgul, Ali
    Models at which not only the asset price but also the volatility are assumed to be stochastic have received a remarkable attention in financial markets. The objective of the current research is to design a numerical method for solving the stochastic volatility (SV) jump-diffusion model of Bates, at which the presence of a nonlocal integral makes the coding of numerical schemes intensive. A numerical implementation is furnished by gathering several different techniques such as the radial basis function (RBF) generated finite difference (FD) approach, which keeps the sparsity of the FD methods but gives rise to the higher accuracy of the RBF meshless methods. Computational experiments are worked out to reveal the efficacy of the new procedure.
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    How to Construct a Fourth-Order Scheme for Heston-Hull-White Equation?
    (Amer Inst Physics, 2019) Akgul, Ali; Soleymani, Fazlollah
    The main objective of the present research is to calculate the weights of a fourth order finite difference (FD) numerical method in option pricing of the financial Heston-Hull-White (HHW) PDE arising in real markets, when in the dynamic of the model, not only the asset price but all the volatility and interest rates are stochastic.
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    Improved numerical solution of multi-asset option pricing problem: A localized RBF-FD approach
    (Pergamon-Elsevier Science Ltd, 2019) Soleymani, Fazlollah; Akgul, Ali
    The objective of this work is to present a novel procedure for tackling European multi-asset option problems, which are modeled mathematically in terms of time-dependent parabolic partial differential equations with variable coefficients. To use as low as possible of number computational grid points, a non-uniform grid is generated while a radial basis function-finite difference scheme with the Gaussian function is applied on such a grid to discretize the model as efficiently as possible. To reduce the burdensome for tackling the resulting set of ordinary differential equations, a Krylov method, which is due to the application of exponential matrix function on a vector, is taken into account. The combination of these techniques reduces the computational effort and the elapsed time. Several experiments are brought froward to illustrate the superiority of the new improved approach. In fact, the contributed procedure is capable to tackle even 6D PDEs on a normally-equipped computer quickly and efficiently. (C) 2019 Elsevier Ltd. All rights reserved.
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    On an improved computational solution for the 3D HCIR PDE in finance
    (Ovidius Univ Press, 2019) Soleymani, Fazlollah; Akgul, Ali; Akgul, Esra Karatas
    The aim of this work is to tackle the three-dimensional (3D) Heston-Cox-Ingersoll-Ross (HCIR) time-dependent partial differential equation (PDE) computationally by employing a non-uniform discretization and gathering the finite difference (FD) weighting coefficients into differentiation matrices. In fact, a non-uniform discretization of the 3D computational domain is employed to achieve the second-order of accuracy for all the spatial variables. It is contributed that under what conditions the proposed procedure is stable. This stability bound is novel in literature for solving this model. Several financial experiments are worked out along with computation of the hedging quantities Delta and Gamma.
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    The existence and uniqueness of solution for linear system of mixed Volterra-Fredholm integral equations in Banach space
    (Amer Inst Mathematical Sciences-Aims, 2020) Hasan, Pakhshan M.; Abdulla, Nejmaddin A.; Soleymani, Fazlollah; Akgul, Ali
    In this paper, a linear system of mixed Volterra-Fredholm integral equations is considered. The problem of existence and uniqueness of its solution is investigated and proved in a complete metric space by using the Banach fixed-point theorem. Also, an iterative method of fixed point type is used to approximate the solution of the system. The algorithm is applied on several examples. To show the accuracy of the results and the efficiency of the method, the approximate solutions are compared with the exact solutions.