Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 80967, 20 pages
doi:10.1155/JAMSA/2006/80967
Abstract
Stochastic differential equations (SDEs) under regime-switching
have recently been developed to model various financial
quantities. In general, SDEs under regime-switching have no
explicit solutions, so numerical methods for approximations have
become one of the powerful techniques in the valuation of
financial quantities. In this paper, we will concentrate on the
Euler-Maruyama (EM) scheme for the typical hybrid mean-reverting
θ-process. To overcome the mathematical difficulties
arising from the regime-switching as well as the non-Lipschitz
coefficients, several new techniques have been developed in this
paper which should prove to be very useful in the numerical
analysis of stochastic systems.