Approximate solvability of forward-backward stochastic differential equations

The solvability of forward-backward stochastic differential equations (FBSD Es for short) has been studied extensively in recent years. To guarantee th e existence and uniqueness of adapted solutions, many different conditions, some quite restrictive, have been imposed. In this paper we propose a new notion: the approximate solvability of FBSDEs, based on the method of optim al control introduced in our primary work [15]. The approximate solvability of a class of FBSDEs is shown under mild conditions; and a general scheme for constructing approximate adapted solutions is proposed.