Quadratic bsdes with mean reflection

Abstract

The present paper is devoted to the study of the well-posedness of BSDEs with mean reflection whenever the generator has quadratic growth in the z argument. This work is the sequel of [6] in which a notion of BSDEs with mean reflection is developed to tackle the super-hedging problem under running risk management constraints. By the contraction mapping argument, we first prove that the quadratic BSDE with mean reflection admits a unique deterministic flat local solution on a small time interval whenever the terminal value is bounded. Moreover, we build the global solution on the whole time interval by stitching local solutions when the generator is uniformly bounded with respect to the y argument.