# Uniqueness, Comparison and Stability for Scalar BSDEs with {Lexp(\mu sqrt(2log(1+L)))}-integrable terminal values and monotonic generators

## TL;DR

This paper studies scalar BSDEs with highly integrable terminal values, establishing uniqueness, comparison, and stability results under extended monotonicity conditions using Girsanov change techniques.

## Contribution

It introduces a novel class of BSDEs with specific integrability conditions and proves key properties under extended monotonicity assumptions.

## Key findings

- Proves uniqueness of solutions for the class of BSDEs.
- Establishes comparison principles for solutions.
- Demonstrates stability under parameter variations.

## Abstract

This paper considers a class of scalar backward stochastic differential equations (BSDEs) with $L\exp(\mu\sqrt{2\log(1+L)})$-integrable terminal values. We associate these BSDEs with BSDEs with integrable parameters through Girsanov change. Using this technique, we prove uniqueness, comparisons and stability for them under an extended monotonicity condition (more precisely one sided Osgood condition).