Reflected Quadratic BSDEs Driven by G-Brownian Motions

Abstract

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

Keywords

G-Brownian motion / G-Martingale / Quandratic growth / G-BSDEs / Probabilistic representation