Two-Moment Decision Models and Expected Utility Maximization: Comment
证明在特定分布限制下，均值标准差模型与期望效用模型产生相同的有效集，扩展了Meyer（1987）的研究，适用于分析风险决策中的有效集一致性。
The two most common approaches to analyzing behavior under uncertainty are the expected utility model (EU) and the meanstandard deviation model (MS). Jack Meyer (1987) has recently established in this Review that when the choice set consists of random variables which are represented by distribution functions that differ from one another only by location and scale parameters, EU and MS are consistent in the sense that any EU ranking of elements of a choice set can also be represented by an MS ranking. No claim has been made by Meyer regarding the EUand MS-efficient sets. However, it can be easily shown that with no additional restrictions, risk-averters' EUefficient set is a subset (in the weak sense) of the MS-efficient set. In this note we extend Meyer's work and prove that under a certain restriction on the support of the distribution, random variables which are MS efficient are also EU efficient, namely, MS and EU yield identical efficient sets. We analyze separately the relationship of MSand EU-efficient sets for all unrestricted (with U'> 0), and alternatively for all risk-averse (with U'> 0 and U < 0). Only pairwise comparisons of risky options are considered.