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:**

- 60G42 Martingales with discrete parameter

**Résumé:** We consider a general discrete time financial market with
proportional transaction costs as in [7] an [12].
In addition to the usual investment in financial assets, we assume
that the agents can invest part of their wealth in industrial
projects that yield a non-linear random return. We study the
problem of maximizing the utility of consumption on a finite time
period. The main difficulty comes from the non-linearity of the
non financial assets' return. Our main result is to show that
existence holds in the utility maximization problem. As an
intermediary step, we prove the closedness of the set $A_T$ of
attainable claims under a {\sl robust no-arbitrage} property
similar to the one introduced in [12] and further
discussed in [7]. This allows us to provide a dual
formulation for $A_T$.

**Mots Clés:** *financial markets with transaction costs ; non-linear returns ; robust no-arbitrage ; super-hedging theorem ; multivariate non-smooth utility maximization*

**Date:** 2004-09-08

**Prépublication numéro:** *PMA-928*