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.

翻译：本文致力于用非利普西茨扩散系数数字解决高维结合的FBSDE。 在温和条件下,我们提供了对任何时间的数值解决方案的后端估计。这一后端估计验证了最近提议的深BSDE方法的趋同。此外,我们开发了一个基于深BSDE方法的数值方案,并在金融市场上提供了数字实例,以显示高性能。