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

TL;DR

This paper establishes the existence and uniqueness of solutions for multi-dimensional reflected G-BSDEs with diagonal generators, using penalization and Picard methods, and explores their link to nonlinear PDE obstacle problems.

Contribution

It introduces new methods to solve multi-dimensional reflected G-BSDEs with diagonal generators and connects these solutions to fully nonlinear PDE obstacle problems.

Findings

Existence and uniqueness of solutions proved.

Methods include penalization and Picard iteration.

Connection established with nonlinear PDE obstacle problems.

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.