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
- 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:** In the context of a general multivariate financial market with transaction
costs, we consider the problem of maximizing expected utility from terminal
wealth. In contrast with the existing literature, where only the liquidation
value of the terminal portfolio is relevant, we consider general utility
functions which are only required to be consistent with the structure
of the transaction costs. An important feature of our analysis is that the
utility function is not required to be $C^1$. Such non-smoothness is suggested
by major natural examples. Our main result is an extension of the well-known
dual formulation of utility maximization problems to this context.

**Mots Clés:** *Utility maximization ; transaction costs ; dual formulation ; nonsmooth analysis*

**Date:** 2000-02-23

**Prépublication numéro:** *PMA-570*