A Complete Ranking of Risky Prospects Consistent with Stochastic Dominance

Abstract

We introduce a new and complete ordering of prospects that is consistent with stochastic dominance (SD). Featuring loss aversion and skewness preference, it mitigates the low discriminatory power of SD and circumvents implementation difficulties associated with third order SD. To highlight its edge, we show that the Aumann-Serrano and the Foster-Hart general riskiness indicators do not conform to third order SD. The ordering we introduce sheds light on mean variance theory and performance measurement, related SD developments, and optimal diversification. Besides, it contributes to the explanation of Rabin's paradox and reconciles the discrepancy between moment preferences and expected utility theory.