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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 90A09 Finance, portfolios, investment
- 90A10 Utility theory
- 49N15 Duality theory
- 49N30 Problems with incomplete information, See also {93C41}

**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