2022/01/02 by Yueyang Zheng, Zheng, Yueyang, Jingtao Shi +1 · 1 citation
Computer Science · Economics, Econometrics and Finance · #49K45 #49N10 #49N70 #60H10 #93E20 #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2201.00314
openalex publication_date 2022/01/02 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
This paper is concerned with a discounted optimal control problem of partially observed forward-backward stochastic systems with jumps on infinite horizon. The control domain is convex and a kind of infinite horizon observation equation is introduced. The uniquely solvability of infinite horizon forward (backward) stochastic differential equation with jumps is obtained and more extended analysis, especially for the backward case, is made. Some new estimates are first given and proved for the critical variational inequality. Then an ergodic maximum principle is obtained by introducing some infinite horizon adjoint equations whose uniquely solvabilities are guaranteed necessarily. Finally, some comparison are made with two kinds of representative infinite horizon stochastic systems and their related optimal controls.