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

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

Optimal consumption in discrete time financial models with industrial investment opportunities and non-linear returns

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Code(s) de Classification MSC:

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