General Mean Reflected Backward Stochastic Differential Equations

The present paper is devoted to the study of backward stochastic differential equations (BSDEs) with mean reflection formulated by Briand et al. (Ann Appl Probab 28(1):482–510, 2018). We investigate the solvability of a generalized mean reflected BSDE, whose driver also depends on the distribution of solution term Y. Using a fixed-point argument, BMO martingale theory and the θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta $$\end{document}-method, we establish existence and uniqueness results for such BSDEs in several typical situations, including the case where the driver is quadratic with bounded or unbounded terminal condition.