Well-posedness for a class of mean field type FBSDEs and classical solutions of related master equations

TL;DR

This paper establishes the well-posedness and regularity of solutions for a class of mean field type FBSDEs and related master equations, providing conditions for existence, uniqueness, and classical solutions.

Contribution

It introduces new monotonicity conditions ensuring well-posedness and regularity of solutions for mean field FBSDEs and master equations, advancing theoretical understanding.

Findings

Proved Lipschitz continuity of the decoupling field.

Established existence and uniqueness of solutions.

Demonstrated regularity and global well-posedness of classical solutions.

Abstract

In this paper, we study a class of mean field type FBSDEs. We propose a class of motonotinity conditions, under which we show the uniformly Lipschitz continuity of the decoupling field and obtain the existence and uniqueness of solution. We further provide a representation result for the solution and the decoupling field. Finally, we obtain the regularity of the decoupling field and establish global well-posedness of classical solutions to related master equations.