Negative Moments, Risk Aversion, and Stochastic Dominance

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Abstract
A simple moment-ordering condition is shown to be necessary for stochastic dominance. Closely related results on generalizations of the geometric and harmonic means are also provided. An ordering of the moment-generating functions is shown to be necessary and sufficient for stochastic dominance. The results have a straightforward and useful interpretation in terms of constant relative and absolute risk aversion utility functions. These results are used to provide necessary and sufficient conditions for optimality of distributions on an important class of utility functions.

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