Minimal Supersolutions of BSDEs with Lower Semicontinuous Generators

TL;DR

This paper investigates the existence and uniqueness of minimal supersolutions for backward stochastic differential equations with generators that are lower semicontinuous, bounded below by an affine function, and satisfy a normalization property.

Contribution

It introduces conditions under which minimal supersolutions of BSDEs with lower semicontinuous generators exist uniquely.

Findings

Proved existence of minimal supersolutions under specified conditions

Established uniqueness of these solutions

Identified key properties of generators ensuring well-posedness

Abstract

We study the existence and uniqueness of minimal supersolutions of backward stochastic differential equations with generators that are jointly lower semicontinuous, bounded below by an affine function of the control variable and satisfy a specific normalization property.