论文标题
概率依赖等级依赖性功能的概率风险规避
Probabilistic risk aversion for generalized rank-dependent functions
论文作者
论文摘要
通过概率混合物中的准转换性定义的概率风险规避是决策分析中常见的有用属性。我们研究了一类的非单调映射，称为广义等级依赖性功能，其中包括预期公用事业，双重公用事业和等级依赖性公用事业的偏好模型，以及在风险管理中使用的签名的Choquet功能。我们的结果充分表征了对广义等级依赖性函数的概率风险厌恶的表征：该属性取决于失真函数，这完全是两种情况之一：凸面和与缩放分位数混合物相对应的情况。我们的结果还导致了七个同等条件，即在双实用程序和签名的Choquet函数的概率混合物中的准分子性。结果，尽管概率风险规避与广义依赖性依赖性函数的经典风险规避概念完全不同，但这两个概念在额外的连续性假设下重合双重公用事业。
Probabilistic risk aversion, defined through quasi-convexity in probabilistic mixtures, is a common useful property in decision analysis. We study a general class of non-monotone mappings, called the generalized rank-dependent functions, which includes the preference models of expected utilities, dual utilities, and rank-dependent utilities as special cases, as well as signed Choquet functions used in risk management. Our results fully characterize probabilistic risk aversion for generalized rank-dependent functions: This property is determined by the distortion function, which is precisely one of the two cases: those that are convex and those that correspond to scaled quantile-spread mixtures. Our result also leads to seven equivalent conditions for quasi-convexity in probabilistic mixtures of dual utilities and signed Choquet functions. As a consequence, although probabilistic risk aversion is quite different from the classic notion of strong risk aversion for generalized rank-dependent functions, these two notions coincide for dual utilities under an additional continuity assumption.
