Wellposedness of reflected G-BSDEs

We provide a complete theory of reflected backward stochastic differential equations driven by G-Brownian motion (reflected G-BSDEs), suggested in Li et al. (2018) [15]. We put forward a new definition of reflected G-BSDEs by introducing a non-Skorohod-type minimality condition. Unlike Li et al. (2018) [15], the alternative formulation of this paper is nice in the sense that it is a natural extension of the definitions of standard G-BSDEs as well as reflected BSDEs. We then prove the existence, uniqueness and some properties of solution under Lipschitz-type assumptions on generator. We also provide some applications including probabilistic interpretation of obstacle problems for fully nonlinear PDEs and super-hedging strategy for American options in nonlinear markets with volatility uncretainty. The key argument is the dynamic programming approach, analyzed in the accompanying paper (O et al. (2023) [22]), and we develop it to the G-expectation framework. Our approach is completely different from the penalization method in Li et al. (2018) [15].