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

Abstract

This paper is dedicated to solving high-dimensional coupled FBSDEs with non-Lipschitz diffusion coefficients numerically. Under mild conditions, we provided a posterior estimate of the numerical solution that holds for any time duration. This posterior estimate validates the convergence of the recently proposed Deep BSDE method. In addition, we developed a numerical scheme based on the Deep BSDE method and presented numerical examples in financial markets to demonstrate the high performance.