Applied Mathematics Seminar

Speaker: Guannan Zhang, Oak Ridge National Lab and Auburn University

Title:   High-Order Numerical Methods for Forward-Backward Stochastic Differential Equations with Jumps and Applications in Nonlocal Diffusion Problems

Abstract: We propose a new numerical scheme for decoupled forward backward stochastic differential equation (FBSDE) with jumps, where the jumps are characterized by Poisson random measures. A variant of Crank-Nicolson scheme is proposed for time discretization. We proved that our scheme can achieve second-order convergence as long as a second-order scheme, e.g. order-2.0 weak Taylor scheme, is used to discretize the forward SDE. A high-order fully discrete scheme is also proposed in the case of Poisson random measures with finite activities. Compared to existing methods, the development of the high-order time-space discretization schemes is the main contribution of this paper. On the other hand, our approach is also an effective tool for nonlocal diffusion problems, where the governing equation is a class of semi-linear partial-integral differential equations.