Three algorithms for solving high-dimensional fully-coupled FBSDEs through deep learning

Abstract

Recently, the deep learning method has been used for solving forward-backward stochastic differential equations (FBSDEs) and parabolic partial differential equations (PDEs). It has good accuracy and performance for high-dimensional problems. In this paper, we mainly solve fully coupled FBSDEs through deep learning and provide three algorithms. Several numerical results show remarkable performance especially for high-dimensional cases.

arXiv comment24 pages, 7 figures

References in corpus (4)

• Solving high-dimensional partial differential equations using deep learning
• Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
• Convergence of the Deep BSDE Method for Coupled FBSDEs
• On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations