Reflected BSDEs with monotone generator

Abstract

We give necessary and sufficient condition for existence and uniqueness of ${\mathbb{L}}^p$-solutions of reflected BSDEs with continuous barrier, generator monotone with respect to $y$ and Lipschitz continuous with respect to $z$, and with data in ${\mathbb{L}}^p$, $p\ge 1$. We also prove that the solutions may be approximated by the penalization method.