Mean Field Forward-Backward Stochastic Differential Equations

TL;DR

This paper establishes an existence result for solutions to fully coupled mean field forward-backward stochastic differential equations, which are fundamental in mean field games and McKean-Vlasov control problems.

Contribution

It provides the first rigorous existence proof for solutions to these complex coupled mean field FBSDEs.

Findings

Existence of solutions for fully coupled mean field FBSDEs.

Applicable to mean field games and McKean-Vlasov control models.

Lays groundwork for future analytical and numerical studies.

Abstract

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.