标题：Two Different Approaches for Optimal Control Problem of Fully Coupled FBSDEs
作者机构：[Shi, Jingtao ] School of Mathematics, Shandong University, Jinan; 250100, China
会议名称：37th Chinese Control Conference, CCC 2018
会议日期：25 July 2018 through 27 July 2018
来源：Chinese Control Conference, CCC
关键词：Dynamic programming principle; Fully coupled FBSDE; Maximum principle; Stochastic optimal control
摘要：This paper is concerned with the optimal control problem, where the recursive cost functional is defined as one of the solution to a controlled fully coupled forward-backward stochastic differential equation (FBSDE), and the control domain is convex. Two different approaches-dynamic programming principle (DPP) and maximum principle (MP)-are applied to solve the problem and the relationship between them are studied. Under some differentiable assumptions, relations among the adjoint processes, the value function and the generalized Hamiltonian function are proved, whereas the diffusion term of the forward equation is independent of the state variable z. The general case for the problem is open. A linear example is discussed as the illustration of our main result. © 2018 Technical Committee on Control Theory, Chinese Association of Automation.