Discretization of forward–backward stochastic differential equations and related quasi-linear parabolic equations

Efficient numerical algorithms for a class of forward–backward stochastic differential equations (FBSDEs) and related quasi-linear parabolic partial differential equations are proposed. The quasi-linear parabolic equation is solved by new layer methods which are constructed by means of a probabilistic approach. The proposed algorithms for solving FBSDEs are based on the four-step scheme of Ma, Protter and Yong. Convergence theorems are proved. Results of some numerical experiments are presented.