Reflected Quadratic BSDEs Driven by G-Brownian Motions

Citation:

Dong CAO,Shanjian TANG.Reflected Quadratic BSDEs Driven by G-Brownian Motions[J].Chinese Annals of Mathematics B,2020,41(6):873~928
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Authors:

Dong CAO; Shanjian TANG

Foundation:

This work was supported by the National Science Foundation of China (No. 11631004) and the Science and Technology Commission of Shanghai Municipality (No. 14XD1400400).
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

Classification:

60H10, 60H30
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