Mean-reflected $G$-BSDEs with multi-variate constraints

Abstract

In this paper, we study the multi-dimensional reflected backward stochastic differential equation driven by $G$-Brownian motion ($G$-BSDE) with a multi-variate constraint on the $G$-expectation of its solution. The generators are diagonally dependent on $Z$ and on all $Y$-components. We obtain the existence and uniqueness result via a fixed-point argumentation.