Quadratic Semimartingale BSDEs under an Exponential Moments Condition

TL;DR

This paper establishes existence, uniqueness, and stability of quadratic semimartingale BSDEs with convex generators under exponential moments, highlighting the role of measure change and limitations of driver convergence.

Contribution

It provides new stability results for quadratic BSDEs under exponential moments, including conditions for measure change and counterexamples for driver convergence.

Findings

Existence and uniqueness of solutions under exponential moments.

Martingale part induces a true change of measure.

Pointwise driver convergence alone does not ensure stability.

Abstract

In the present article we provide existence, uniqueness and stability results under an exponential moments condition for quadratic semimartingale backward stochastic differential equations (BSDEs) having convex generators. We show that the martingale part of the BSDE solution defines a true change of measure and provide an example which demonstrates that pointwise convergence of the drivers is not sufficient to guarantee a stability result within our framework.