Properties of solution for fully coupled fractional mean-field forward-backward stochastic differential equation

Abstract

We consider a fully coupled fractional mean-field forward-backward stochastic differential equation (MF-FBSDE) whose coefficients not only depend on the solution triple (X, Y, Z) but also on its distribution. We prove the existence of a unique solution for such MF-FBSDEs. In addition, we also prove the weak monotonicity and Lipschitz’s continuity and a comparison theorem.