Stability of backward stochastic differential equations: the general Lipschitz case

Antonis Papapantoleon; Dylan Possamaï; Alexandros Saplaouras

doi:10.1214/23-EJP939

Stability of backward stochastic differential equations: the general Lipschitz case

Antonis Papapantoleon, Dylan Possamaï, Alexandros Saplaouras

Applied Probability

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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.

Original language	English
Article number	51
Number of pages	56
Journal	Electronic Journal of Probability
Volume	28
DOIs	https://doi.org/10.1214/23-EJP939
Publication status	Published - 2023

Keywords

BSDE
nonlinear martingale representations
processes with jumps
random time horizon
stability
stochas-tically discontinuous martingales
stochastic Lipschitz generator

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23-EJP939Final published version, 644 KBLicence: CC BY

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AB - 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.

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KW - processes with jumps

KW - random time horizon

KW - stability

KW - stochas-tically discontinuous martingales

KW - stochastic Lipschitz generator

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ER -

Stability of backward stochastic differential equations: the general Lipschitz case

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