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Fractional Degree Stochastic Dominance

Rachel J. Huang (), Larry Y. Tzeng () and Lin Zhao ()
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Rachel J. Huang: Department of Finance, National Central University, Taoyuan 32001, Taiwan; Center for Research in Econometric Theory and Applications, National Taiwan University, Taipei 10617, Taiwan; Risk and Insurance Research Center, National Chengchi University, Taipei 11605, Taiwan;
Larry Y. Tzeng: Center for Research in Econometric Theory and Applications, National Taiwan University, Taipei 10617, Taiwan; Risk and Insurance Research Center, National Chengchi University, Taipei 11605, Taiwan; Department of Finance, National Taiwan University, Taipei 10617, Taiwan;
Lin Zhao: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 Beijing, China

Management Science, 2020, vol. 66, issue 10, 4630-4647

Abstract: We develop a continuum of stochastic dominance rules for expected utility maximizers. The new rules encompass the traditional integer-degree stochastic dominance; between adjacent integer degrees, they formulate the consensus of individuals whose absolute risk aversion at the corresponding integer degree has a negative lower bound. By extending the concept of “uniform risk aversion” previously proposed in the literature to high-order risk preferences, we interpret the fractionalized degree parameter as a benchmark individual relative to whom all considered individuals are uniformly no less risk averse in the lottery choices. The equivalent distribution conditions for the new rules are provided, and the fractional degree “increase in risk” is defined. We generalize the previously defined notion of “risk apportionment” and demonstrate its usefulness in characterizing comparative statics of risk changes in fractional degrees.

Keywords: stochastic dominance; risk aversion; risk lovingness; higher-order risk preferences; risk taking (search for similar items in EconPapers)
Date: 2020
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