A decomposition approach for the discrete-time approximation of FBSDEs with a jump
Résumé
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 w.r.t. the variable z. We propose a recursive scheme based on a general existence result given in the companion paper [15] 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. Keywords: discrete-time approximation, forward-backward SDE, Lipschitz generator, generator of quadratic growth, progressive enlargement of filtrations, decomposition in the reference filtration. MSC classification (2010): 65C99, 60J75, 60G57.
Domaines
Probabilités [math.PR]| Origine | Fichiers produits par l'(les) auteur(s) |
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