Convergence of the Deep BSDE method for FBSDEs with non-Lipschitz coefficients

This paper is dedicated to solve high-dimensional coupled FBSDEs with non-Lipschitz diffusion coefficients numerically. Under mild conditions, we provide a posterior estimate of the numerical solution which holds for arbitrary time duration. This posterior estimate justifies the convergence of the recently proposed Deep BSDE method. We also construct a numerical scheme based on the Deep BSDE method and present numerical examples in financial markets to show the high performance.