In this talk, we present a deep learning method for solving high-dimensional stochastic optimal control problems driven by fully coupled forward–backward stochastic differential equations (FBSDEs). We begin with a brief overview of recent advances in deep learning methods for solving high-dimensional FBSDEs and stochastic optimal control problems. We then reformulate the control problem driven by fully coupled FBSDEs as a stochastic Stackelberg differential game problem (a leader-follower problem). In the following, we develop a bi-level optimization algorithm in which the leader’s and follower’s cost functionals are optimized alternately using deep neural networks. Finally, we apply the proposed algorithm to two investment–consumption examples under stochastic recursive utility, and the numerical results demonstrate the effectiveness of the proposed method.
