Existence of an optimal control for a system driven by a degenerate coupled forward-backward stochastic differential equations

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• 作者：Khaled Bahlali^a ; ^{bahlali@univ-tln.fr} ; Omar Kebiri^b ; ^{o_kebiri@yahoo.fr} ; Ahmed Mtiraoui^a ; ^c ; ^{mtiraoui@univ-tln.fr}
• 刊名：Comptes Rendus Mathematique
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：355
• 期：1
• 页码：84-89
• 全文大小：272 K
• 卷排序：355

文摘

We establish the existence of an optimal control for a system driven by a coupled forward–backward stochastic differential equation (FBDSE) whose diffusion coefficient may degenerate (i.e. are not necessary uniformly elliptic). The cost functional is defined as the initial value of the backward component of the solution. We construct a sequence of approximating controlled systems, for which we show the existence of a sequence of feedback optimal controls. By passing to the limit, we get the existence of a feedback optimal control. Filippov's convexity condition is used to ensure that the optimal control is strict. The present result extends those obtained in  and  to controlled systems of coupled SDE–BSDE.