Approximate solvability of forward-backward stochastic differential equations via method of optimal control

Motivated by some problems from mathematical finance and stochastic maximum principle, the solvability of forward-backward stochastic differential equations (FBSDE, for short) has been studied extensively in recent years. To guarantee the existence and uniqueness of adapted solutions, many different conditions, some are quite restrictive, have been imposed. In this paper we propose a new notion: the approximate solvability of FBSDEs, based on the method of optimal control introduced in our primary work. The approximate solvability of a class of FBSDEs is shown under mild conditions