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.