论文标题
关于平均方差标准和随机优势标准的等效性
On The Equivalence Of The Mean Variance Criterion And Stochastic Dominance Criteria
论文作者
论文摘要
我们研究了两个彩票的最大预期效用标准（MEUC），研究均值方差标准（MVC）等效的必要条件。根据Chamberlain（1983），我们得出结论，MVC等于在任何对称椭圆分布下的二阶随机优势规则（SSDR）。然后，我们讨论Schuhmacher等人的工作。 （2021）。尽管他们的理论发现推断出均值变化分析在偏斜分布下仍然有效，但我们认为这并不意味着MVC与SSDR一致。实际上，产生多个MV对，遵循偏差正常的分布，很明显，对于某些规避风险的投资者，MVC与SSDR不一致。在这项工作的第二部分中，我们研究了Levy and Markowitz（1979）的前提：“ MVC在任何近似二次的效用函数下，推断了投资者预期效用的最大化，而没有对彩票的分布做出任何进一步的假设”。使用Monte Carlo模拟，我们发现大约二次效用函数的集合太窄。具体而言，我们的仿真表明$ \ log {（a+z）} $和$（1+z）^a $几乎是二次的，而$ -e^{ - a（1+z）} $和$ - （1+z）^{ - a} $在极端的值或稳定的pareto pareto分配中都无法大致近似于近似的效用。
We study the necessary and sufficient conditions under which the Mean-Variance Criterion (MVC) is equivalent to the Maximum Expected Utility Criterion (MEUC), for two lotteries. Based on Chamberlain (1983), we conclude that the MVC is equivalent to the Second-order Stochastic Dominance Rule (SSDR) under any symmetric Elliptical distribution. We then discuss the work of Schuhmacher et al. (2021). Although their theoretical findings deduce that the Mean-Variance Analysis remains valid under Skew-Elliptical distributions, we argue that this does not entail that the MVC coincides with the SSDR. In fact, generating multiple MV-pairs that follow a Skew-Normal distribution it becomes evident that the MVC fails to coincide with the SSDR for some types of risk-averse investors. In the second part of this work, we examine the premise of Levy and Markowitz (1979) that "the MVC deduces the maximization of the expected utility of an investor, under any approximately quadratic utility function, without making any further assumption on the distribution of the lotteries". Using Monte Carlo Simulations, we find out that the set of approximately quadratic utility functions is too narrow. Specifically, our simulations indicate that $\log{(a+Z)}$ and $(1+Z)^a$ are almost quadratic, while $-e^{-a(1+Z)}$ and $-(1+Z)^{-a}$ fail to approximate a quadratic utility function under either an Extreme Value or a Stable Pareto distribution.
