Quadratic Mean-Field Reflected BSDEs

TL;DR

This paper studies quadratic mean-field reflected backward stochastic differential equations, establishing existence and uniqueness results using advanced mathematical techniques, and extends these results to unbounded conditions for specific generator types.

Contribution

It introduces a novel approach combining linearization, BMO martingale theory, and a $ heta$-method to analyze quadratic mean-field reflected BSDEs with unbounded terminal conditions.

Findings

Proved existence and uniqueness for bounded terminal conditions and obstacles.

Extended results to unbounded cases for concave or convex generators.

Developed a successive approximation method for unbounded scenarios.

Abstract

In this paper, we analyze mean-field reflected backward stochastic differential equations when the driver has quadratic growth in the second unknown $z$. Using linearization technique and BMO martingale theory, we first apply fixed point argument to establish uniqueness and existence result for the case with bounded terminal condition and obstacle. Then, with the help of a $\theta$-method, we develop a successive approximation procedure to remove the boundedness condition on the terminal condition and obstacle when the generator is concave (or convex) with respect to the 2nd unknown $z$