2018/03/06 by Mingshang Hu, Hu, Mingshang, Shaolin Ji +3 · 3 citations
Economics, Econometrics and Finance · #Climate Change Policy and Economics #FOS: Mathematics #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1803.02109
openalex publication_date 2018/03/06 · openalex created_date 2018/03/29 · openalex updated_date 2026/07/28
We study a stochastic optimal control problem for fully coupled forward-backward stochastic control systems with a nonempty control domain. For our problem, the first-order and second-order variational equations are fully coupled linear FBSDEs. Inspired by Hu (Hu, Probability, Uncertainty and Quantitative Risk, 2(1) (2017):pp 1-20), we develop a new decoupling approach by introducing an adjoint equation which is a quadratic BSDE. By revealing the relations among the terms of the first-order Taylor's expansions, we estimate the orders of them and derive a global stochastic maximum principle which includes a completely new term. Applications to stochastic linear quadratic control problems are investigated.