Stability of backward stochastic differential equations: the general case

TL;DR

This paper establishes stability results for backward stochastic differential equations with jumps in a very general setting, showing that solutions converge when data sequences do, thus unifying various approximation frameworks.

Contribution

It extends existing stability results for BSDEs to a more general framework with jumps and multiple filtrations, unifying several numerical approximation approaches.

Findings

Solutions of BSDEs with jumps are stable under data convergence.

The results unify different frameworks for numerical approximation of BSDEs.

The paper generalizes stability results beyond previous specific cases.

Abstract

In this paper, we obtain stability results for backward stochastic differential equations with jumps (BSDEs) in a very general framework. More specifically, we consider a convergent sequence of standard data, each associated to their own filtration, and we prove that the associated sequence of (unique) solutions is also convergent. The current result extends earlier contributions in the literature of stability of BSDEs and unifies several frameworks for numerical approximations of BSDEs and their implementations.