Fully coupled McKean-Vlasov forward-backward SDEs driven by mixed Brownian motions

Abstract

In this paper, we prove the existence and uniqueness of a solution for a general McKean-Vlasov fully coupled forward-backward stochastic differential equation driven by mixed Brownian motions, where the coefficients depend, nonlinearly, on both the state process as well as of its probability law. Using the continuation method, we establish our results under suitable conditions.