An efficient numerical method for forward-backward stochastic differential equations driven by G-Brownian motion

Abstract

In this paper, we study the numerical method for solving forward-backward stochastic differential equations driven by G-Brownian motion (G-FBSDEs) which correspond to fully nonlinear partial differential equations (PDEs). First, we give an approximate conditional G-expectation and obtain some feasible methods to calculate the distribution of G-Brownian motion. On this basis, some efficient numerical schemes for G-FBSDEs are then proposed. We rigorously analyze the errors of the proposed schemes and prove the convergence. Finally, several numerical experiments are presented to demonstrate the accuracy of our schemes.