Solutions for Functional Fully Coupled Forward-Backward Stochastic Differential Equations

Abstract: In this paper, we study a functional fully coupled forward-backward stochastic differential equations (FBSDEs). Under a new type of integral Lipschitz and monotonicity conditions, the existence and uniqueness of solutions for functional fully coupled FBSDEs is proved. We also investigate the relationship between the solution of functional fully coupled FBSDE and the classical solution of the path-dependent partial differential equation (P-PDE). When the solution of the P-PDE has some smooth and regular properties, we solve the related functional fully coupled FBSDE and prove the P-PDE has a unique solution.