Existence of an optimal control for a coupled FBSDE with a non degenerate diffusion coefficient |
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Authors: | K Bahlali O Kebiri B Mezerdi |
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Institution: | 1. IMATH, Université de Toulon , La Garde Cedex, France.;2. Laboratory of Probability and Statistics, Tlemcen University , Tlemcen, Algeria.;3. Laboratoire de Mathématiques Appliquées, Université Mohamed Khider , Biskra, Algeria. |
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Abstract: | We consider a controlled system driven by a coupled forward–backward stochastic differential equation with a non degenerate diffusion matrix. The cost functional is defined by the solution of the controlled backward stochastic differential equation, at the initial time. Our goal is to find an optimal control which minimizes the cost functional. The method consists to 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 establish the existence of a relaxed optimal control to the initial problem. The existence of a strict control follows from the Filippov convexity condition. |
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Keywords: | Optimal control forward–backward stochastic differential equations stochastic control Hamilton–Jacobi–Bellman equation relaxed control strict control |
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