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.

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Corresponding authors

Correspondence to Dong Cao or Shanjian Tang.

Additional information

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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Cite this article

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

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Keywords

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

2000 MR Subject Classification

  • 60H10
  • 60H30