Optimal control of a class of fully coupled forward-backward stochastic partial differential equations  

作　　者：Suya Zhang Maozhong Xu Qingxin Meng 

机构地区：[1]School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China [2]School of Mathematical Sciences,Zhejiang Normal University,Jinhua 321004,China [3]School of Sciences,Huzhou University,Huzhou 313000,China

出　　处：《Probability, Uncertainty and Quantitative Risk》2025年第1期67-102,共36页概率、不确定性与定量风险(英文)

基　　金：Qingxin Meng was supported by the Key Projects of Natural Science Foundation of Zhejiang Province(Grant No.LZ22A010005);the National Natural Science Foundation of China(Grant Nos.12271158 and 11871121).

摘　　要：This paper investigates the optimal control problem for a class of fully coupled forward-backward stochastic partial differential equations(FBSPDEs).Based on the existence of a unique solution to such equations,we formulated the associated optimal control problem within a convex control domain.By employing the convex variational method,we derive the associated stochastic maximum'principle(SMP)for the optimal control problem intrinsic to this system.Finally,to demonstrate the applicability of our theoretical results,we apply SMP to a class of linear quadratic problems and obtain explicit expressions for the unique optimal control.

关 键 词：Forward-backward stochastic partial differential equation Monotonicity condition Stochastic maximum principle Convex domain Linear quadratic problem 

分 类 号：O232[理学—运筹学与控制论]