Efficient portfolios in financial markets with proportional transaction costs

Luciano Campi (), Elyès Jouini () and Vincent Porte
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Luciano Campi: LAGA - Laboratoire Analyse, Géométrie et Applications - UP8 - Université Paris 8 Vincennes-Saint-Denis - UP13 - Université Paris 13 - Institut Galilée - CNRS - Centre National de la Recherche Scientifique
Vincent Porte: Crédit Agricole - Crédit Agricole

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Abstract: In this article, we characterize efficient portfolios, i.e. portfolios which are optimal for at least one rational agent, in a very general financial market model of foreign currencies with proportional transaction costs. In our setting, transaction costs may be random, time dependent, have jumps and the preferences of the agents are modeled by multivariate expected utility functions. Thanks to the dual formulation of expected multivariate utility maximization problem established in Campi and Owen, we provide a complete characterization of efficient portfolios, generalizing earlier results of Dybvig and Jouini and Kallal. We basically show that a portfolio is efficient if and only if it is cyclically anticomonotonic with respect to at least one consistent price system. Finally, we introduce the notion of utility price of a given contingent claim as the minimal amount of a given initial portfolio allowing any agent to reach the claim by trading in the market, and give a dual representation of it.

Keywords: Cyclic anticomonotonicity; utility maximization; proportional transaction costs; duality; utility price.; utility price (search for similar items in EconPapers)
Date: 2013-06-01
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00664074v1
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Citations: View citations in EconPapers (2)

Published in Mathematics and Financial Economics, 2013, 7 (3), pp.281-304. ⟨10.1007/s11579-013-0099-4⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00664074

DOI: 10.1007/s11579-013-0099-4

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