Quadratic BSDEs with mean reflection driven by G-brownian motion

Abstract

In this paper, the well-posedness of a kind of backward stochastic differential equation driven by [Formula: see text]-Brownian motions ([Formula: see text]-BSDEs for short) with mean reflection is investigated. In particular, the generator is allowed having quadratic growth in [Formula: see text]. Combining a representation of the solution with [Formula: see text]-BMO martingale techniques, fixed point argument, and [Formula: see text]-method, existence and uniqueness results for such [Formula: see text]-BSDEs are provided under bounded and unbounded terminal condition.