The Optimal Control of Fully-Coupled Forward-Backward Doubly Stochastic Systems Driven by Itô-Lévy Processes
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This paper studies the optimal control of a fully-coupled forward-backward doubly stochastic system driven by Itô-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.
KeywordsForward-backward doubly stochastic differential equations Itô-Lévy processes linear quadratic problem maximum principle variational equation
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