Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Discrete time approximation and Monte-Carlo simulation of backward stochastic differential equations

Auteur(s):

Code(s) de Classification MSC:

Résumé: We suggest a discrete-time approximation for decoupled forward-backward stochastic differential equations. The $L^p$ norm of the error is shown to be of the order of the time step. Given a simulation-based estimator of the conditional expectation operator, we then suggest a backward simulation scheme, and we study the induced $L^p$ error. This estimate is more investigated in the context of the Malliavin approach for the approximation of conditional expectations. Extensions to the reflected case are also considered.

Mots Clés: Monte-Carlo methods for (reflected) forward-backward SDE's ; Malliavin calculus ; regression estimation

Date: 2002-11-15

Prépublication numéro: PMA-776

Pdf file : PMA-776.pdf