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Evaluation of Double Average Asian Options by the legendre spectral method

Journal of Shanghai University(English Edition) 2003年第3期7卷 206-213页

作者：盛慧莉马和平 Department of Mathematics College of Sciences Shanghai University Shanghai 200072 China

In this paper, the evaluation of discretely sampled Asian options was considered by numerically solving the associated partial differential equations with the legendre spectral method. Double average options were discussed as examples. The problem is a parabolic one on a finite domain whose equation degenerates into ordinary differential equations on the boundaries. A fully discrete scheme was established by using the legendre spectral method in space and the Crank-Nicolson finite difference scheme in time. The stability and convergence of the scheme were analyzed. Numerical results show that the method can keep the spectral accuracy in space for such degenerate problems.

关键词： double average Asian options discretely sampled arithmetic Asian options legendre spectral method degenerate parabolic problem.

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A Stochastic Collocation method for Delay Differential Equations with Random Input

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Advances in Applied Mathematics and Mechanics 2014年第4期6卷 403-418页

作者： Tao Zhou Institute of Computational Mathematics Academy of Mathematics and Systems SciencesThe Chinese Academy of SciencesBeijing 100190China

In this work,we concern with the numerical approach for delay differential equations with random coefficients.We first show that the exact solution of the problem considered admits good regularity in the random space,provided that the given data satisfy some reasonable assumptions.A stochastic collocation method is proposed to approximate the solution in the random space,and we use the legendre spectral collocation method to solve the resulting deterministic delay differential equations.Convergence property of the proposed method is analyzed.It is shown that the numerical method yields the familiar exponential order of convergence in both the random space and the time space.Numerical examples are given to illustrate the theoretical results.

关键词： Delay differential equations stochastic collocation sparse grid legendre spectral method

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