论文标题
一种深度学习方法，用于解决由完全耦合的FBSDE驱动的随机最佳控制问题
A deep learning method for solving stochastic optimal control problems driven by fully-coupled FBSDEs
论文作者
论文摘要
在本文中，我们主要关注由完全耦合的前回向随机微分方程（简称FBSDE）驱动的高维随机最佳控制问题的数值解决方案。我们首先将问题转换为随机的Stackelberg差异游戏问题（领导者追随者问题），然后开发出BI级优化方法，在领导者的成本功能和追随者的成本功能中，通过深层神经网络进行了优化。至于数值结果，我们计算了通过随机递归实用程序模型解决的两个投资消费问题的示例，这两个示例的结果都证明了我们提出的算法的有效性。
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.
