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

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

A large deviations approach to optimal long term investment


Code(s) de Classification MSC:

Résumé: We study an optimal investment model in which the goal is to maximize the large deviation probability that the long term growth rate will overperform a given target level. This criterion can be considered as an asymptotic dynamic control version of the familiar Value at Risk (VaR) concept. The optimal logarithmic moment gene\-rating function is explicitly derived from an infinite time horizon risk sensitive control problem. A careful study of its domain and its behavior at the boundary of the domain is required. We then use large deviations techniques for stating the optimal rate function of the long term growth rate. This measure of upside-risk provides in turn an objective probabilistic interpretation of the usually subjective degree of risk aversion in CRRA utility function.

Mots Clés: Large deviation ; risk sensitive control ; dynamic programming equation ; optimal logarithmic moment generating function ; long term growth rate ; optimal portfolio

Date: 2001-01-09

Prépublication numéro: PMA-633