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Forward-Backward Stochastic Differential Equations and Controlled McKean Vlasov Dynamics

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 نشر من قبل Francois Delarue
 تاريخ النشر 2013
  مجال البحث
والبحث باللغة English
 تأليف Rene Carmona




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The purpose of this paper is to provide a detailed probabilistic analysis of the optimal control of nonlinear stochastic dynamical systems of the McKean Vlasov type. Motivated by the recent interest in mean field games, we highlight the connection and the differences between the two sets of problems. We prove a new version of the stochastic maximum principle and give sufficient conditions for existence of an optimal control. We also provide examples for which our sufficient conditions for existence of an optimal solution are satisfied. Finally we show that our solution to the control problem provides approximate equilibria for large stochastic games with mean field interactions.



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