Reflected Quadratic BSDEs driven by $G$-Brownian Motions

Dong Cao; Shanjian Tang

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arXiv · 1906.00583

Reflected Quadratic BSDEs driven by $G$-Brownian Motions

Dong Cao·Shanjian Tang

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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.

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Dong Cao, Shanjian Tang. 2019-06-03. Reflected Quadratic BSDEs driven by $G$-Brownian Motions. https://arxiv.org/abs/1906.00583

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