Existence, uniqueness and approximation for $L^p$ solutions of reflected BSDEs under weaker assumptions

TL;DR

This paper establishes new existence and uniqueness results for $L^p$ solutions of reflected backward stochastic differential equations (BSDEs) with continuous barriers, under weaker assumptions than previously known, and demonstrates solution approximation methods.

Contribution

It introduces weaker conditions for existence and uniqueness of solutions to reflected BSDEs and explores growth conditions related to barriers, improving upon prior results.

Findings

Established necessary and sufficient growth conditions for barriers.

Proved solutions can be approximated via penalization and solution sequences.

Extended the class of generators satisfying weaker assumptions.

Abstract

We put forward and prove several existence and uniqueness results for $L^p\ (p>1)$ solutions of reflected BSDEs with continuous barriers and generators satisfying a one-sided Osgood condition together with a general growth condition in $y$ and a uniform continuity condition or a linear growth condition in $z$. A necessary and sufficient condition with respect to the growth of barrier is also explored to ensure the existence of a solution. And, we show that the solutions may be approximated by the penalization method and by some sequences of solutions of reflected BSDEs. Our results improve considerably some known works.