General Mean Reflected BSDEs

TL;DR

This paper studies generalized mean reflected backward stochastic differential equations (BSDEs) with drivers depending on the solution's distribution, establishing existence and uniqueness results using advanced probabilistic techniques.

Contribution

It introduces a solvability framework for mean reflected BSDEs with distribution-dependent drivers, including quadratic cases, using fixed-point, BMO martingale, and $ heta$-method techniques.

Findings

Proved existence and uniqueness of solutions for generalized mean reflected BSDEs.

Extended solvability results to quadratic drivers with various terminal conditions.

Developed a methodological approach applicable to complex distribution-dependent BSDEs.

Abstract

The present paper is devoted to the study of backward stochastic differential equations with mean reflection formulated by Briand et al. [7]. We investigate the solvability of a generalized mean reflected BSDE, whose driver also depends on the distribution of the solution term $Y$. Using a fixed-point argument, BMO martingale theory and the $\theta$-method, we establish the existence and uniqueness result for such BSDEs in several typical situations, including the case where the driver is quadratic with bounded or unbounded terminal condition.