| Université Paris 6 Pierre et Marie Curie | Université Paris 7 Denis Diderot | |
| CNRS U.M.R. 7599 | ||
| ``Probabilités et Modèles Aléatoires'' | ||
Auteur(s):
Code(s) de Classification MSC:
Résumé: Given a multi-dimensional Markov diffusion $X$, the Malliavin integration by parts formula provides a family of representations of the conditional expectation $E[g(X_2)|X_1]$. The different representations are determined by some {\it localizing functions}. We discuss the problem of variance reduction within this family. We characterize an exponential function as the unique integrated-variance minimizer among the class of separable localizing functions. For general localizing functions, we provide a PDE characterization of the optimal solution, if it exists. This allows to draw the following observation~: the separable exponential function does not minimize the integrated variance, except for the trivial one-dimensional case. We provide an application to a portfolio allocation problem, by use of the dynamic programming principle.
Mots Clés: Monte Carlo ; Malliavin calculus ; calculus of variations
Date: 2002-02-12
Prépublication numéro: PMA-709
Pdf file : PMA-709.pdf