A priori estimates for multidimensional BSDEs with integrable data

TL;DR

This paper establishes a priori estimates and stability results for multidimensional backward stochastic differential equations with integrable terminal data and generators that are non-increasing and Lipschitz continuous, expanding understanding of solutions under minimal integrability conditions.

Contribution

It introduces new a priori estimates and stability results for multidimensional BSDEs with merely integrable data, relaxing growth restrictions on the generator.

Findings

Derived a priori estimates for solutions.

Proved stability of solutions under integrable data.

Extended analysis to multidimensional BSDEs with minimal assumptions.

Abstract

We study Backward Stochastic Differential Equations on a probability space equipped with a Brownian filtration. We assume that the terminal value and the generator at zero are merely integrable. Moreover, the generator is assumed to be non-increasing with respect to the value variable (with no restrictions on the growth) and Lipschitz continuous, with sublinear growth, with respect to the control variable. We provide a priori estimate and stability result for solutions to the aforementioned BSDEs.