Mean-preserving Portfolio Dominance

Consider risk-averse agents with utility functions U and V holding portfolios composed of the same two (risky and riskless) assets. Then, V is (Arrow) more risk averse if in all such portfolios V invests less in the risky asset. A natural extension of this analysis of attitudes towards risk to risk itself is to establish a relation between distributions which is necessary and sufficient to induce such investment patterns in the class of all risk-averse agents. This characterization is established in this paper for distributions with equal means. Second Degree Dominance performs a similar role for the notion of ‘more risk averse’ introduced by Pratt but it is too weak for the Arrow concept.