In this paper, we point out the role of anticomonotonicity in the characterization of efficient contingent claims, and in the measure of inefficiency size of financial strategies. Two random variables are said to be anticomonotonic if they move in opposite directions. We first provide necessary and sufficient conditions for a contingent claim to be efficient in markets, which might be with frictions in a quite general framework. We then compute a measure of inefficiency size for any contingent claim. We finally give several applications of these results, studying in particular the efficiency of superreplication strategies.

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 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 [3], we provide a complete characterization of efficient portfolios, generalizing earlier results of Dybvig [10] and Jouini and Kallal [16]. 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.

In this article, we characterize e¢cient contingent claims in a context of transaction costs and multidimensional utility functions. The dual formulation of utility maximization helps us outline the key notion of cyclic anticomonotonicity. Moreover, after de…ning a utility price in this multidimensional setting, we provide a measure of strategies inef…ciency and a tool allowing to e¤ectively compute this measure with the help of cyclic anticomonotonicity.