Open Access
2023 Stability of backward stochastic differential equations: the general Lipschitz case
Antonis Papapantoleon, Dylan Possamaï, Alexandros Saplaouras
Author Affiliations +
Electron. J. Probab. 28: 1-56 (2023). DOI: 10.1214/23-EJP939

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.

Funding Statement

Antonis Papapantoleon gratefully acknowledges the financial support from the Hellenic Foundation for Research and Innovation Grant No. HFRI-FM17-2152. Dylan Possamaï gratefully acknowledges the financial support from the ANR project PACMAN (ANR-16-CE05-0027). Alexandros Saplaouras gratefully acknowledges the financial support from the DFG Research Training Group 1845 “Stochastic Analysis with Applications in Biology, Finance and Physics”. Moreover, all authors gratefully acknowledge the financial support from the Procope project “Financial markets in transition: mathematical models and challenges”.

Citation

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Antonis Papapantoleon. Dylan Possamaï. Alexandros Saplaouras. "Stability of backward stochastic differential equations: the general Lipschitz case." Electron. J. Probab. 28 1 - 56, 2023. https://doi.org/10.1214/23-EJP939

Information

Received: 4 August 2022; Accepted: 24 March 2023; Published: 2023
First available in Project Euclid: 5 April 2023

arXiv: 2107.11048
Digital Object Identifier: 10.1214/23-EJP939

Subjects:
Primary: 60F15 , 60F17 , 60F25 , 60G048 , 60G05 , 60G07 , 60G44 , 60G57 , 60H05 , 60H20

Keywords: BSDE , nonlinear martingale representations , processes with jumps , random time horizon , stability , stochastic Lipschitz generator , stochastically discontinuous martingales

Vol.28 • 2023
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