Moment conditions for fractional degree stochastic dominance

The fractional degree stochastic dominance provides a continuum of stochastic dominance rules for ranking uncertain prospects, which encompasses usual integer-degree cases. This work presents its moment conditions. Specifically, the necessary conditions are provided based on the ordering of the moment-generating functions of distributions, which can be related to expected utility with constant absolute risk aversion preferences. We consider numerically many well-known distributions including normal distribution, gamma distribution and so on to show that the moment conditions are simple and computationally feasible in practical applications. We also apply our conditions to detect portfolio efficiency.