Existence of optimal solutions for a stochastic control problems for systems of mean-field FBSDEs
Professor Boulakhras Gherbal from the University of Biskra, Algeria will give a seminar lecture with the following title:
“Existence of optimal solutions for a stochastic control problems for systems of mean-field FBSDEs”
In this work, we prove firstly the existence of a strong optimal strict control for systems driven by linear forward-backward stochastic differential equations of mean-field type (MF-FBSDEs), where the coefficients of the system depend on the state process and also on the distribution of the state process. The cost functions are assumed to be convex. We derive also necessary and sufficient conditions for the existence of optimal controls for this linear stochastic control problem. Secondly, where the system is governed by a nonlinear FBSDEs of mean field type, we prove the existence of optimal relaxed control as well as optimal strict control and we establish also necessary and sufficient optimality conditions for both relaxed and strict control problems.