# Reflected Quadratic BSDEs driven by $G$-Brownian Motions

## TL;DR

This paper studies reflected quadratic G-Brownian motion driven backward stochastic differential equations, establishing existence, uniqueness, and linking solutions to nonlinear PDEs via a nonlinear Feynman-Kac formula.

## Contribution

It introduces a method for solving reflected quadratic G-BSDEs and connects these solutions to fully nonlinear PDEs in a Markovian setting.

## Key findings

- Existence of solutions via the penalty method
- Uniqueness of solutions through a priori estimates
- Nonlinear Feynman-Kac formula linking G-BSDEs and PDEs

## Abstract

In this paper, we consider a reflected backward stochastic differential equation driven by a $G$-Brownian motion ($G$-BSDE), with the generator growing quadratically in the second unknown. We obtain the existence by the penalty method, and a priori estimates which implies the uniqueness, for solutions of the $G$-BSDE. Moreover, focusing our discussion at the Markovian setting, we give a nonlinear Feynman-Kac formula for solutions of a fully nonlinear partial differential equation.