Reflected BSDEs driven by G-Brownian motion with non-Lipschitz coefficients

TL;DR

This paper studies reflected backward stochastic differential equations driven by G-Brownian motion with non-Lipschitz coefficients, establishing existence, uniqueness, and comparison results using iterative and penalization methods.

Contribution

It extends the theory of reflected G-BSDEs to coefficients satisfying beta-order Mao's condition, providing new existence and comparison results.

Findings

Existence of solutions via Picard iteration and penalization methods.

Uniqueness of solutions under beta-order Mao's condition.

Comparison theorem for reflected G-BSDEs.

Abstract

In this paper, we consider the reflected backward stochastic differential equations driven by G-Brownian motion (reflected G-BSDEs) whose coefficients satisfy the beta-order Mao's condition. The uniqueness is obtained by some a priori estimates and the existence can be proved by two different methods. The first one is Picard iteration and the second one is approximation via penalization. The latter construction is useful to get the comparison theorem.