Solution to Forward-Backward Stochastic Differential Equations With Random Coefficients and Application to Deterministic Optimal Control

• 成果类型: Article
• 署名作者: Li, Hongdan; Xu, Juanjuan; Zhang, Huanshui
• 署名单位: Shandong University of Science & Technology; Shandong University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3144331
• 发表日期: 2022
• 页码: 6888-6895
• 关键词: Index Terms-Coupled stochastic Riccati-type differential equa-tions; Discretization; linear coupled forward-backward stochastic differential equations (FBSDEs); random coefficients

摘要

We address forward-backward stochastic differential equations (FBSDEs) with random coefficients. Differently from previous approaches, we consider FBSDEs with coefficients that are random and correlated with forward and backward variables. In addition, expectation terms appear in the forward equation, and this makes challenging to solve coupled FBSDEs, e.g., those coming from corporations' fiscal policy planning. Using a discretization approach, an analytic solution to the FBSDEs is given in terms of coupled stochastic Riccati-type differential equations. We also apply our results to optimal deterministic control problem for Ito stochastic systems with both random and deterministic coefficients. Our results show that the discretization approach is a powerful tool to decouple complex FBSDEs.