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

Abstract : 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.
Document type :
Preprints, Working Papers, ...
2011
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00576922
Contributor : Thomas Lim <>
Submitted on : Monday, November 26, 2012 - 7:37:50 PM
Last modification on : Friday, February 10, 2017 - 1:13:09 AM
Document(s) archivé(s) le : Wednesday, February 27, 2013 - 3:47:54 AM

Files

FBSDE-Lipschitz.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00576922, version 3
  • ARXIV : 1103.3029

Collections

Citation

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

Share

Metrics

Record views

190

Document downloads

57