Fractional Degree Stochastic Dominance
为期望效用最大化者开发了一套连续的随机占优规则，涵盖传统整数阶占优，并通过分数阶参数刻画个体风险厌恶程度，定义了分数阶“风险增加”及其比较静态分析。
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. This paper was accepted by David Simchi-Levi, decision analysis.