Efficient portfolios in financial markets with proportional transaction costs

Mathematics and Financial Economics - Tập 7 - Trang 281-304 - 2013
Luciano Campi1,2, Elyès Jouini3,4,5, Vincent Porte6
1LAGA, Université Paris 13, Villetaneuse, France
2CREST, Université Paris 13, Malakoff, France
3IFD, Université Paris-Dauphine, Paris, France
4CEREMADE, Paris, France
5Institut Universitaire de France, Paris, France
6Risk Management Group, Paris, France

Tóm tắt

In this article, we characterize efficient portfolios, i.e. portfolios which are optimal for at least one rational agent, in a very general multi-currency financial market model 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. We provide a complete characterization of efficient portfolios, generalizing earlier results of Dybvig (Rev Financ Stud 1:67–88, 1988) and Jouini and Kallal (J Econ Theory 66: 178–197, 1995). 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 that prices it. 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, and give a dual representation of it as the largest proportion of the market price necessary for all agents to reach the same expected utility level.

Tài liệu tham khảo

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