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

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  • Gao, Jianwei
  • Zhao, Feng

Abstract

This paper develops some new stochastic dominance (SD) rules for ranking transformations on a random variable, which is the first time to study ranking approach for transformations on the discrete framework. By using the expected utility theory, the authors first present a sufficient condition for general transformations by first degree SD (FSD), and further develop it into the necessary and sufficient condition for the monotonic transformations. For the second degree SD (SSD) case, the authors divide the monotonic transformations into increasing and decreasing ones, and respectively derive the necessary and sufficient conditions for the two situations. For two different discrete random variables with the same possible states, they obtain the sufficient and necessary condition for FSD and SSD, respectively. The feature of the new SD rules is that 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 existing SD approach where they are described by cumulative distribution functions. In this way, the authors construct a new theoretical paradigm for transformations on the discrete random variable. Finally, a numerical example is provided to show the effectiveness of the new SD rules.

Suggested Citation

  • Gao, Jianwei & Zhao, Feng, 2016. "A new approach of stochastic dominance for ranking transformations on the discrete random variable," Economics Discussion Papers 2016-49, Kiel Institute for the World Economy (IfW Kiel).
    • Handle: RePEc:zbw:ifwedp:201649
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    References listed on IDEAS

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    1. 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.
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    More about this item

    Keywords

    stochastic dominance; transformation; utility theory; insurance;
    All these keywords.

    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
    • G1 - Financial Economics - - General Financial Markets

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