Date
2015
Ville de l'éditeur
Paris
Indexation documentaire
Analyse
Subject
Discrete-time approximation; forward-backward SDE; Lipschitz generator; decomposition in the reference ltration; progressive enlargement of ltrations
Nom de la revue
Random Operators and Stochastic Equations
Volume
23
Numéro
2
Date de publication
2015
Pages article
81-109
Nom de l'éditeur
De Gruyter
Auteur
Kharroubi, Idris
Lim, Thomas
Type
Article accepté pour publication ou publié
Résumé en anglais
We are concerned with the discretization of a solution of a forward-backward stochastic differential equation (FBSDE) with a jump process depending on the Brownian motion. In this paper, we study the cases of Lipschitz generators and the generators with a quadratic growth with respect to the variable z. We propose a recursive scheme based on a general existence result given in the companion paper [Journal of Theoretical Probability 27 (2014), 683–724] and we study the error induced by the time discretization. We prove the convergence of the scheme when the number of time steps n goes to infinity. Our approach allows to get a convergence rate similar to that of schemes of Brownian FBSDEs