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.