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Résumé :
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In my thesis, we are interested by the existence of optimal solutions of a stochastic control problem for systems driven by nonlinear forward-backward stochastic differential equations of mean-field type (MF-FBSDEs). The coefficients of the system depend on the state process, and also on the distribution of the state process, via the expectation of some function of the state. The cost functional is also of mean-field type. In the first chapter, we prove existence of a strong optimal strict control and we derive also necessary as well as sufficient optimality conditions for the existence of optimal controls for this linear stochastic control problem. In the second chapter, we prove the existence of optimal relaxed control as well as optimal strict control for nonlinear MF-FBSDEs and we establish in the fourth chapter necessary and sufficient optimality conditions for both relaxed and strict control problems for this case. In the last chapter, we prove the existence of optimal relaxed control as well as optimal strict control for nonlinear MF-FBSDEs with controlled diffusion.
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