FBSDEs Approach for Solving Discrete-Time Rational Expectations Model With State Delays

• 成果类型: Article
• 署名作者: Ma, Tianfu; Xu, Juanjuan; Wang, Wei; Zhang, Huanshui
• 署名单位: Shandong University; Shandong University of Science & Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3328513
• 发表日期: 2024
• 页码: 1744-1751
• 关键词: mathematical models; DELAYS; Stochastic processes; Nash equilibrium; HISTORY; Delay effects; White noise; Explicit solution; Forward and backward stochastic difference equations (FBSDEs); rational expectations model; state delay

摘要

In this article, we consider the discrete-time rational expectations model with state delays. In particular, the dynamic equation relies both on the history of states and the conditional expectation of the future states. The novelty of this article lies in transforming the solvability of the rational expectations model to that of the forward and backward stochastic difference equations (FBSDEs). The main contribution is to obtain the (unique) solvability and the explicit solutions for the FBSDEs in both finite horizon and infinite horizon. This accordingly gives the explicit solution of the rational expectations model. The key technology is to establish a nonhomogeneous relationship between forward and backward processes of the FBSDEs.