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.
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This work was supported by the National Science Foundation of China (No. 11631004) and the Science and Technology Commission of Shanghai Municipality (No. 14XD1400400).
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Cao, D., Tang, S. Reflected Quadratic BSDEs Driven by G-Brownian Motions. Chin. Ann. Math. Ser. B 41, 873–928 (2020). https://doi.org/10.1007/s11401-020-0238-1
- G-Brownian motion
- Quandratic growth
- Probabilistic representation
2000 MR Subject Classification