The Optimal Control of Fully Coupled Forward Backward Doubly Stochastic Systems Driven by Ito Levy Processes
This paper studies the optimal control of a fully coupled forward backward doubly stochastic system driven by Ito Levy 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.
J. Syst. Sci. Complex.