Reflected BSDEs driven by G-Brownian motion with time-varying Lipschitz coefficients

Abstract

In this paper, we consider the reflected backward stochastic differential equations driven by $G$-Brownian motion (reflected $G$-BSDEs) with time-varying Lipschitz coefficients. We obtain the uniqueness result by establishing a priori estimates. For the existence, the solution can be approximated by a family of reflected $G$-BSDEs with Lipschitz conditions and by penalized $G$-BSDEs with time-varying coefficients. The latter approximation is useful to get the comparison theorem. Finally, we study the reflected $G$-BSDEs with infinite time horizon.