2023/04/09 by Jingtao Lin, Lin, Jingtao, Jingtao Shi +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #35K15 #60H10 #93E20 #Climate Change Policy and Economics #FOS: Mathematics #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2304.04136
openalex publication_date 2023/04/09 · openalex created_date 2023/04/12 · openalex updated_date 2026/07/28
This paper is concerned with a kind of risk-sensitive optimal control problem for fully coupled forward-backward stochastic systems. The control variable enters the diffusion term of the state equation and the control domain is not necessarily convex. A new global maximum principle is obtained without assuming that the value function is smooth. The maximum condition, the first- and second-order adjoint equations heavily depend on the risk-sensitive parameter. An optimal control problem with a fully coupled linear forward-backward stochastic system and an exponential-quadratic cost functional is discussed. The optimal feedback control and optimal cost are obtained by using Girsanov's theorem and completion-of-squares approach via risk-sensitive Riccati equations. A local solvability result of coupled risk-sensitive Riccati equations is given by Picard-Lindelof's Theorem.