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.
Bibliographical noteFunding Information:
The authors would like to thank the editor and anonymous referee for providing valuable suggestions which have led to significant improvement of this article. This work is supported by MOE (Ministry of Education in China) Project of Humanities and Social Sciences under Research Project 19YJC790125 , Philosophy and Social Science Grant of Jiangsu Province, China under Research Project No. 2020SJZDA070 and the National Natural Science Foundation of China with Grant Numbers 71901123 , 72141304 .
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- Stochastic dominance
- Moment-generating functions
- Gamma distribution