A deep learning method for solving stochastic optimal control problems driven by fully-coupled FBSDEs
This addresses numerical solution challenges for high-dimensional stochastic optimal control problems in finance, though it appears incremental as it builds on existing deep learning approaches for FBSDEs.
The paper tackles high-dimensional stochastic optimal control problems driven by fully-coupled forward-backward stochastic differential equations (FBSDEs) by transforming them into a stochastic Stackelberg differential game and developing a bi-level optimization method using deep neural networks. The results demonstrate effectiveness on two investment-consumption problem examples with stochastic recursive utility models.
In this paper,we mainly focus on the numerical solution of high-dimensional stochastic optimal control problem driven by fully-coupled forward-backward stochastic differential equations (FBSDEs in short) through deep learning. We first transform the problem into a stochastic Stackelberg differential game problem (leader-follower problem), then a bi-level optimization method is developed where the leader's cost functional and the follower's cost functional are optimized alternatively via deep neural networks. As for the numerical results, we compute two examples of the investment-consumption problem solved through stochastic recursive utility models, and the results of both examples demonstrate the effectiveness of our proposed algorithm.