A decomposition approach for the discrete-time approximation of FBSDEs with a jump I : the Lipschitz case

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Date
2011
Titre de la collection
Cahier de recherche CEREMADE, Université Paris-Dauphine
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https://hal.archives-ouvertes.fr/hal-00576922
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Analyse
Subject
Discrete-time approximation; forward-backward SDE; Lipschitz generator; progressive enlargement of ltrations; decomposition in the reference ltration
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https://basepub.dauphine.fr/handle/123456789/17338
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Auteur
Kharroubi, Idris
Lim, Thomas
Type
Document de travail / Working paper
Nombre de pages du document
28
Résumé en anglais
We study the discrete-time approximation for solutions of forward-backward stochas- tic dierential equations (FBSDEs) with a jump. In this part, we study the case of Lipschitz generators, and we refer to the second part of this work [15] for the quadratic case. Our method is based on a result given in the companion paper [14] which allows to link a FBSDE with a jump with a recursive system of Brownian FBSDEs. Then we use the classical results on discretization of Brownian FBSDEs to approximate the recursive system of FBSDEs and we recombine these approximations to get a dis- cretization of the FBSDE with a jump. This approach allows to get a convergence rate similar to that of schemes for Brownian FBSDEs.