This paper studies the optimal control of a fully-coupled forward-backward doubly stochastic system driven by Ito-Lévy processes under partial information.The existence and uniqueness of the solution are obtained...This paper studies the optimal control of a fully-coupled forward-backward doubly stochastic system driven by Ito-Lévy processes under partial information.The existence and uniqueness of the solution are obtained for a type of fully-coupled forward-backward doubly stochastic differential equations(FBDSDEs in short).As a necessary condition of the optimal control,the authors get the stochastic maximum principle with the control domain being convex and the control variable being contained in all coefficients.The proposed results are applied to solve the forward-backward doubly stochastic linear quadratic optimal control problem.展开更多
基金supported by the Cultivation Program of Distinguished Young Scholars of Shandong University under Grant No.2017JQ06the National Natural Science Foundation of China under Grant Nos.11671404,11371374,61821004,61633015the Provincial Natural Science Foundation of Hunan under Grant No.2017JJ3405
文摘This paper studies the optimal control of a fully-coupled forward-backward doubly stochastic system driven by Ito-Lévy processes under partial information.The existence and uniqueness of the solution are obtained for a type of fully-coupled forward-backward doubly stochastic differential equations(FBDSDEs in short).As a necessary condition of the optimal control,the authors get the stochastic maximum principle with the control domain being convex and the control variable being contained in all coefficients.The proposed results are applied to solve the forward-backward doubly stochastic linear quadratic optimal control problem.
