A type of general FBSDEs and anticipated backward linear quadratic stochastic optimal control problems

We prove the existence and the uniqueness of the solutions of a new type of general forward-backward stochastic differential equations (FBSDEs), where the forward equations are Itô stochastic delayed ones and the backward equations are anticipated back stochastic differential equations, under some certain “monotonicity” conditions. By using the solutions of the FBSDEs we discuss the anticipated backward linear quadratic optimal stochastic control problems.