Partial Moments and Negative Moments in Ordering Asymmetric Distributions
Moment ordering condition is shown to be necessary for stochastic dominance. In this paper related results of the partial moments and negative moments are presented. The condition for any degree of stochastic dominance, by ordering fractional and negative moments of the distribution, will be shown. We present the sufficient condition for restricted families of distribution functions - a class of asymmetric distributions. Additionally we present a related general measure based on fractional moments, which can be used for complete ordering the set of distributions. The condition applies generally, subject only to the requirement that the moments exist. The result rests on the fact that the negative and the fractional moments of the distribution can be interpreted as constant relative risk aversion utility function.
KeywordsUtility Function Portfolio Selection Stochastic Dominance Constant Relative Risk Aversion Lorenz Dominance
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