Constant Risk Aversion, the Dual Theory, and the Gini Inequality Index

Abstract

Constant risk aversion means that adding the same constant to all outcomes of two distributions, or multiplying all their outcomes by the same positive constant, will not change the preference relation between them. In this paper we prove several representation theorems, where constant risk aversion is combined with some other known axioms to imply specific functional forms. Among other things, we obtain a form of disappointment aversion theory without using the concept of reference point in the axioms and a form of the rank dependent modelwithout making any reference to the ranking of the outcomes. This axiomatization leads to a natural generalization of the Gini inequality index. Our analysis also establishes a connection between constant risk aversion. Frechet differentiability, and orders of risk aversion.

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