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

TL;DR

This paper proves the convergence of the Deep BSDE method for high-dimensional FBSDEs with non-Lipschitz coefficients and demonstrates its effectiveness through numerical experiments in financial applications.

Contribution

It provides a posterior convergence estimate for the Deep BSDE method under mild conditions, extending its applicability to non-Lipschitz coefficients.

Findings

Posterior estimate validates convergence

Numerical scheme demonstrates high accuracy

Effective in financial market simulations

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.