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Coherent Diversi cation Measures in Portfolio Theory: An Axiomatic Foundation by Gilles Boevi Koumou


This paper provides an axiomatic foundation of the measurement of diversi cation in a one-period portfolio theory under the assumption that the investor has complete information about the joint distribution of asset returns.

Four categories of portfolio diversi cation measures can be distinguished: the law of large numbers diversi cation measures, the correlation diversi cation measures, the market portfolio diversi cation measures and the risk contribution diversi cation measures.

The authors propose the fi rst step towards a rigorous theory of correlation diversi cation measures. They propose a set of nine desirable axioms for this class of diversi cation measures, and name the measures satisfying these axioms coherent diversi cation measures that they distinguish from the notion of coherent risk measures.

They provide the decision-theoretic foundations of their axioms by studying their compatibility with investors' preference for diversi cation in two important decision theories under risk: the expected utility theory and Yaari's dual theory.

They explore whether useful methods of measuring portfolio diversi cation satisfy their axioms. They also investigate whether or not their axioms have forms of representation.

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