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A new approach of stochastic dominance for ranking transformations on the discrete random variable


  • Gao, Jianwei
  • Zhao, Feng


This paper presents some new stochastic dominance (SD) criteria for ranking transformations on a random variable, which is the first time that this is done for transformations under the discrete framework. By using the expected utility theory, the authors first propose a sufficient condition for general transformations by first degree SD (FSD), and further develop it into the necessary and sufficient condition for monotonic transformations. For the second degree SD (SSD) case, they divide the monotonic transformations into increasing and decreasing categories, and further derive their necessary and sufficient conditions, respectively. For two different discrete random variables with the same possible states, the authors obtain the sufficient and necessary conditions for FSD and SSD, respectively. The new SD criteria have the following features: each FSD condition is represented by the transformation functions and each SSD condition is characterized by the transformation functions and the probability distributions of the random variable. This is different from the classical SD approach where FSD and SSD conditions are described by cumulative distribution functions. Finally, a numerical example is provided to show the effectiveness of the new SD criteria.

Suggested Citation

  • Gao, Jianwei & Zhao, Feng, 2017. "A new approach of stochastic dominance for ranking transformations on the discrete random variable," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 11, pages 1-23.
  • Handle: RePEc:zbw:ifweej:201714

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    References listed on IDEAS

    1. Valentini, Edilio, 2015. "Indirect taxation, public pricing and price cap regulation: A synthesis," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 9, pages 1-39.
    2. Larry Y. Tzeng & Rachel J. Huang & Pai-Ta Shih, 2013. "Revisiting Almost Second-Degree Stochastic Dominance," Management Science, INFORMS, vol. 59(5), pages 1250-1254, May.
    3. Chiu, W.Henry, 2005. "Degree of downside risk aversion and self-protection," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 93-101, February.
    4. Ilia Tsetlin & Robert L. Winkler & Rachel J. Huang & Larry Y. Tzeng, 2015. "Generalized Almost Stochastic Dominance," Operations Research, INFORMS, vol. 63(2), pages 363-377, April.
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    More about this item


    stochastic dominance; transformation; utility theory; insurance;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty


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