Almost first-degree stochastic dominance for transformations and its application in insurance strategy

Almost stochastic dominance is a relaxation of stochastic dominance, which allows small violations of stochastic dominance rules to avoid situations where most decision makers prefer one alternative to another but stochastic dominance cannot rank them. The authors first discuss the relations between almost first-degree stochastic dominance (AFSD) and the second-degree stochastic dominance (SSD), and demonstrate that the AFSD criterion is helpful to narrow down the SSD efficient set. Since the existing AFSD criterion is not convenient to rank transformations of random variables due to its relying heavily on cumulative distribution functions, the authors propose the AFSD criterion for transformations of random variables by means of transformation functions and the probability function of the original random variable. Moreover, they employ this method to analyze the transformations resulting from insurance and option strategy.几乎随机占优（Almost Stochastic Dominance）是随机占优（Stochastic Dominance）的一种松弛形式，其允许小幅违反随机占优规则，以规避多数决策者更偏好某一方案却无法通过随机占优对二者进行排序的情形。研究者首先探讨了一阶几乎随机占优（Almost First-degree Stochastic Dominance，以下简称AFSD）与二阶随机占优（Second-degree Stochastic Dominance，以下简称SSD）之间的关联，并证明一阶几乎随机占优准则有助于缩小二阶随机占优有效集的范围。鉴于现有一阶几乎随机占优准则过度依赖累积分布函数，难以便捷地对随机变量的变换进行排序，研究者借助变换函数与原随机变量的概率函数，提出了适用于随机变量变换的一阶几乎随机占优准则。此外，他们还运用该方法分析了保险与期权策略所引发的变换。