Doubly reflected backward SDEs driven by G-Brownian motions and fully nonlinear PDEs with double obstacles

Abstract In this paper, we introduce a new method to study the doubly reflected backward stochastic differential equation driven by G -Brownian motion ( G -BSDE). Our approach involves approximating the solution through a family of penalized reflected G -BSDEs with a lower obstacle that are monotone decreasing. By employing this approach, we establish the well-posedness of the solution of the doubly reflected G -BSDE with the weakest known conditions, and uncover its relationship with the fully nonlinear partial differential equation with double obstacles for the first time.