Abstract and Applied Analysis
Volume 2013 (2013), Article ID 750147, 8 pages
http://dx.doi.org/10.1155/2013/750147
Research Article

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

Yanli Zhou,1 Yonghong Wu,1 Xiangyu Ge,2 and B. Wiwatanapataphee3

1Department of Maths and Statistics, Curtin University, Perth, WA 6845, Australia
2School of Statistics & Maths, Zhongnan University of Economics and Law, Wuhan 430073, China
3Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand

Received 1 December 2012; Revised 13 March 2013; Accepted 14 March 2013

Academic Editor: Xinguang Zhang

Copyright © 2013 Yanli Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.