Lp-solutions of multi-dimensional BSDEs with mean reflection

Abstract

The present paper focuses on the investigation of multi-dimensional mean reflected backward stochastic differential equations (BSDEs) in a possibly non-convex reflection domain, whose generator also depends on the marginal probability distributions of the solution $(Y,Z)$. Our main idea is to decompose the mean reflected BSDE into a BSDE and a deterministic Skorokhod problem. Then, utilizing $L^p$-estimates for BSDEs and Skorokhod problems, we explore the solvability of $L^p$-solutions ($p>1$) through fixed-point argument and an approximation approach under both inward normal and oblique reflection scenarios.