Stochastic Dominance and Absolute Risk Aversion

In this paper, we propose the infimum of the Arrow–Pratt index of absolute risk aversion as a measure of global risk aversion of a utility function. We show that, for any given arbitrary pair of distributions, there exists a threshold level of global risk aversion such that all increasing concave utility functions with at least as much global risk aversion would rank the two distributions in the same way. Furthermore, this threshold level is sharp in the sense that, for any lower level of global risk aversion, we can find two utility functions in this class yielding opposite preference relations for the two distributions.This paper has benefited from insightful comments made by James Mirrless, two anonymous referees, and by seminar participants at IAE and Simposio de Análisis Económico in Salamanca. They should not bear any responsibility for the remaining errors. Financial support from the Spanish Ministry of Education and Science and FEDER through grants SEC2003-306 and SEC2003-1961, from the Generalitat of Catalonia through the Barcelona Economics program (CREA) and grants 2005SGR00447 and 2005SGR00626 is gratefully acknowledged. This paper is part of the “Polarization and Conflict” project, contract 3CIT2-CT-2004-506084 funded by the European Commission.