Multi-dimensional BSDEs driven by G-Brownian motion and related system of fully nonlinear PDEs

Abstract

In this paper, we study the well-posedness of multi-dimensional backward stochastic differential equations driven by G-Brownian motion (G-BSDEs). The existence and uniqueness of solutions are obtained via a contraction argument for Y component and a backward iteration of local solutions. Furthermore, we show that, the solution of multi-dimensional G-BSDE in a Markovian framework provides a probabilistic formula for the viscosity solution of a system of nonlinear parabolic partial differential equations.

Keywords:

• G-expectation
• G-Brownian motion
• multi-dimensional BSDEs
• fully nonlinear PDEs

Acknowledgments

The author is grateful to Dr. Mingshang Hu and Dr. Falei Wang for their fruitful discussions. The author would also like to thank the anonymous referee for the valuable comments and constructive suggestions which improved the presentation of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

Research supported by the National Natural Science Foundation of China (No. 11601282 and No. 11671231) and the Natural Science Foundation of Shandong Province (No. ZR2016AQ10).