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A Robust Weak Taylor Approximation Scheme for Solutions of Jump-Diffusion Stochastic Delay Differential Equations

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  • Yanli Zhou
  • Yonghong Wu
  • Xiangyu Ge
  • B. Wiwatanapataphee

Abstract

Stochastic delay differential equations with jumps have a wide range of applications, particularly, in mathematical finance. Solution of the underlying initial value problems is important for the understanding and control of many phenomena and systems in the real world. In this paper, we construct a robust Taylor approximation scheme and then examine the convergence of the method in a weak sense. A convergence theorem for the scheme is established and proved. Our analysis and numerical examples show that the proposed scheme of high order is effective and efficient for Monte Carlo simulations for jump-diffusion stochastic delay differential equations.

Suggested Citation

  • Yanli Zhou & Yonghong Wu & Xiangyu Ge & B. Wiwatanapataphee, 2013. "A Robust Weak Taylor Approximation Scheme for Solutions of Jump-Diffusion Stochastic Delay Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, April.
    • Handle: RePEc:hin:jnlaaa:750147
    DOI: 10.1155/2013/750147
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