A Posteriori Estimate for a Class of Mean-Field Forward-backward Stochastic Differential Equations

We study the numerical solutions for a class of coupled mean-field forward-backward stochastic differential equations. Under suitable regularity assumptions, a posteriori estimate of forward-backward stochastic differential equation is provided. This posterior estimate indicates that the error of the solution for the forward-backward equation can be controlled by the error of the terminal term. Furthermore, we propose a numerical algorithm based on deep neural network and conduct convergence analysis on the discretization scheme.