Mean field forward-backward stochastic differential equations. (English) Zbl 1297.93182

Carmona, René; Delarue, François

Electron. Commun. Probab. 18, Paper No. 68, 15 p. (2013).

Summary: 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.

MSC:

93E20	Optimal stochastic control
60H30	Applications of stochastic analysis (to PDEs, etc.)
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60F99	Limit theorems in probability theory

Keywords:

FBSDEs; mean field interactions