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

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

Wealth-path dependent utility maximization in incomplete markets

Auteur(s):

Code(s) de Classification MSC:

Résumé: Motivated by an optimal investment problem under time horizon uncertainty and when default may occurs, we study a general structure for an incomplete semimartingale model extending the classical terminal wealth utility maximization problem. This modelling leads to the formulation of a wealth path-dependent utility maximization problem. Our main result is an extension of the well-known dual formulation to this context. Sufficient conditions for characterizing the optimal solution are also provided in the case of complete markets, and are illustrated by examples.

Mots Clés: Utility maximization ; random time horizon ; wealth path dependent utility ; incomplete markets ; convex duality

Date: 2002-10-23

Prépublication numéro: PMA-767

Pdf file : PMA-767.pdf