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

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).