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

Idris Kharroubi (1, 2) , Thomas Lim (3, 4)

1 CREST - Centre de Recherche en Économie et Statistique
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 LAP - Laboratoire Analyse et Probabilités
4 ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise

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.

Keywords: Discrete-time approximation; forward-backward SDE; Lipschitz generator; progressive enlargement of ltrations; decomposition in the reference ltration

Domains: Analysis of PDEs [math.AP]

Idris Kharroubi, Thomas Lim. A decomposition approach for the discrete-time approximation of FBSDEs with a jump I : the Lipschitz case. 2011. ⟨hal-00576922v3⟩