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:**

- 90A09 Finance, portfolios, investment
- 93E20 Optimal stochastic control
- 49J52 Nonsmooth analysis (other weak concepts of optimality), See also {58C20, 90C48}
- 60H30 Applications of stochastic analysis (to PDE, etc.)
- 90A16 Dynamic economic models, growth models

**Résumé:** We study the dual formulation of the utility maximization problem
in incomplete markets when the utility function is finitely
valued on the whole real line. We extend the existing results in
this literature in two directions. First, we allow for nonsmooth
utility functions, so as to include the shortfall minimization
problems in our framework. Secondly, we allow for the presence of
some given liability, or a random endowment. In particular, these
results provide a dual formulation of the utility indifference
valuation rule.

**Mots Clés:** *utility maximization ; incomplete markets ; convex duality*

**Date:** 2002-03-15

**Prépublication numéro:** *PMA-712*

**Pdf file : **PMA-712.pdf