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1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

Abstract : 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 $A T$.

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





Autor: Bruno Bouchard - Huyên Pham -

Fuente: https://hal.archives-ouvertes.fr/



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