Multi-dimensional reflected BSDEs driven by $G$-Brownian motion with diagonal generators

Abstract

We consider the well-posedness problem of multi-dimensional reflected backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs) with diagonal generators. Two methods, i.e., the penalization method and the Picard iteration argument, are provided to prove the existence and uniqueness of solutions. We also study its connection with the obstacle problem of a system of fully nonlinear PDEs.