On the Regularity of a Weak Formulation of Stochastic Differential Mean-Field Games

TL;DR

This paper investigates the regularity properties of a weak McKean-Vlasov FBSDE related to stochastic mean-field games, focusing on classical and Malliavin differentiability to deepen theoretical understanding.

Contribution

It provides new regularity results for a weak formulation of McKean-Vlasov FBSDEs in the context of mean-field games, extending existing theoretical frameworks.

Findings

Established classical differentiability of the McKean-Vlasov FBSDE

Proved Malliavin differentiability under certain conditions

Enhanced understanding of regularity in mean-field game models

Abstract

We study a McKean-Vlasov Forward-Backward Stochastic Differential Equation (FBSDE) in connection with the theory of Stochastic Differential Mean-Field games, particularly the weak (non-fully coupled) formulation described in Section 3.3.1 of the book "Probabilistic theory of mean field games with applications" by Carmona and Delarue. Our main goal is to obtain regularity results for this McKean-Vlasov FBSDE, specifically classical and Malliavin differentiability