Solvability of a class of mean-field BSDEs with quadratic growth

TL;DR

This paper investigates the solvability of multi-dimensional mean-field backward stochastic differential equations with quadratic growth, establishing existence, uniqueness, and comparison results under small terminal conditions.

Contribution

It introduces new methods to prove existence and uniqueness for multi-dimensional mean-field BSDEs with quadratic growth, a problem not fully addressed before.

Findings

Existence and uniqueness under small terminal value

Comparison theorem for mean-field BSDEs with quadratic growth

New analytical methods developed for multi-dimensional cases

Abstract

In this paper, we study the multi-dimensional mean-field backward stochastic differential equations (BSDEs, for short) with quadratic growth. Under small terminal value, the existence and uniqueness are proved for the multi-dimensional situation when the generator f(t,Y,E[Y],Z,E[Z]) is of quadratic growth with respect to the last four items, using some new methods. Besides, a kind of comparison theorem is obtained.