Reflected BSDEs with monotone generator

TL;DR

This paper establishes necessary and sufficient conditions for the existence and uniqueness of solutions to reflected backward stochastic differential equations with monotone generators, and shows these solutions can be approximated via penalization methods.

Contribution

It provides a complete characterization for solutions of reflected BSDEs with monotone generators and demonstrates an effective approximation approach.

Findings

Characterization of existence and uniqueness conditions

Solutions can be approximated by penalization methods

Applicable for data in b1p, p b1 1

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.