The purpose of this note is to provide an existence result for the solution of fully coupled Forward Backward Stochastic Differential Equations (FBSDEs) of the mean field type. These equations occur in the study of mean field games and the optimal control of dynamics of the McKean Vlasov type.
René Carmona. François Delarue. "Mean field forward-backward stochastic differential equations." Electron. Commun. Probab. 18 1 - 15, 2013. https://doi.org/10.1214/ECP.v18-2446