2024/05/16 by Fan Wu, Xun Li, Wu, Fan +3
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #93E03 #93E15 #FOS: Mathematics #Opinion Dynamics and Social Influence #Optimization and Control (math.OC) #Stochastic processes and financial applications #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2405.10083
openalex publication_date 2024/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper investigates an inhomogeneous non-zero-sum linear-quadratic (LQ, for short) differential game problem whose state process and cost functional are regulated by a Markov chain. Under the L2 stabilizability framework, we first provide a sufficient condition to ensure the L2-integrability of the state process and study a class of linear backward stochastic differential equation (BSDE, for short) in infinite horizon. Then, we seriously discuss the LQ problem and show that the closed-loop optimal control is characterized by the solutions to coupled algebra Riccati equations (CAREs, for short) with some stabilizing conditions and a linear BSDE. Based on those results, we further analyze the non-zero-sum stochastic differential game problem and give the closed-loop Nash equilibrium through the solution to a system of two cross-coupled CAREs and two cross-coupled BSDEs. Finally, some related numerical