For addressing the Allis-type anomalies, a fractional degree reference dependent stochastic dominance rule is developed which is a generalization of the integer degree reference dependent stochastic dominance rules. This new rule can effectively explain why the risk comparison does not satisfy translational invariance and scaling invariance in some cases. The rule also has a good property that it is compatible with the endowment effect of risk. This rule can help risk-averse but not absolute risk-averse decision makers to compare risks relative to reference points. We present some tractable equivalent integral conditions for the fractional degree reference dependent stochastic dominance rule, as well as some practical applications for the rule in economics and finance.

为了解决Allis型异常，开发了分数度参考依赖随机优势规则，它是整数度参考依赖随机优势规则的推广。这个新规则可以有效地解释为什么风险比较在某些情况下不满足平移不变性和尺度不变性。该规则还具有与风险禀赋效应相容的良好性质。该规则可以帮助规避风险但不是绝对规避风险的决策者比较风险相对于参考点的风险。我们提出了分数度参考依赖随机优势规则的一些易于处理的等价积分条件，以及该规则在经济学和金融学中的一些实际应用。