Existence of a stochastic optimal control for systems driven by FBSDEs

Khaled Bahlali (1) , Boulekhrass Gherbal (2) , Brahim Mezerdi (2)

1 IMATH - Institut de Mathématiques de Toulon - EA 2134
2 BISKRA - Université Mohamed Khider de Biskra

We prove the existence of optimal relaxed controls as well as strict optimal controls for systems governed by non linear forward–backward stochastic differential equations (FBSDEs). Our approach is based on weak convergence techniques for the associated \FBSDEs\ in the Jakubowski S-topology and a suitable Skorokhod representation theorem.

Mots clés: Forward backward stochastic differential equation

Domaines: Probabilités [math.PR]; Systèmes et contrôle [cs.SY]; Equations aux dérivées partielles [math.AP]

Khaled Bahlali, Boulekhrass Gherbal, Brahim Mezerdi. Existence of a stochastic optimal control for systems driven by FBSDEs. Systems and Control Letters, 2011, 60 (5), pp.344 - 349. ⟨10.1016/j.sysconle.2011.02.011⟩. ⟨hal-01297356⟩