Systems of BSDEs with oblique reflection and related optimal switching problems

TL;DR

This paper establishes the existence of solutions for systems of BSDEs with oblique reflection driven by an increasing function, under minimal assumptions, and applies these results to optimal switching problems.

Contribution

It introduces a new framework for systems of BSDEs with oblique reflection on general probability spaces, extending previous results and providing solutions under weaker conditions.

Findings

Existence of solutions for integrable terminal conditions.

Solutions under minimal assumptions on the probability space.

Application to optimal switching problems.

Abstract

We consider systems of backward stochastic differential equations with c\`adl\`ag upper barrier $U$ and oblique reflection from below driven by an increasing continuous function $H$. Our equations are defined on general probability spaces with a filtration satisfying merely the usual assumptions of right continuity and completeness. We assume that the pair $(H(U),U)$ satisfies a Mokobodzki--type condition. We prove the existence of a solution for integrable terminal conditions and integrable quasi--monotone generators. Applications to the optimal switching problem are given.