摘要翻译：
大多数经济学和统计学中的理性决策模型是由冯·诺依曼和摩根斯坦、萨维奇等人公理的期望效用理论(EU)。然而，在金融经济学和数学金融学中，情况就不是这样了，在这些领域，投资决策通常基于Markowitz在20世纪50年代引入的均值-方差(MV)方法。在MV框架下，每一个可用的投资机会（“资产”）或投资组合只在两个维度上表示，即从该投资中预期的财务回报的事前均值和标准差$(\\mu，\\sigma)$。实用工具的拥护者认为，一般来说，MV方法在逻辑上是不一致的。最著名的是，挪威保险理论家Borch提出了一个证明，表明二维MV无差异曲线不能代表理性投资者的偏好（他声称MV无差异曲线“不存在”）。这就是众所周知的博奇悖论，并产生了一个重要的，但通常鲜为人知的哲学文献，将MV与欧盟联系起来。我们考察了对这一文献的主要早期贡献，集中在博奇的逻辑和它被搁置的论点上。
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英文标题：
《Mean-Variance and Expected Utility: The Borch Paradox》
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作者：
David Johnstone, Dennis Lindley
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最新提交年份：
2013
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分类信息：

一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Quantitative Finance 数量金融学
二级分类：General Finance 一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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英文摘要：
The model of rational decision-making in most of economics and statistics is expected utility theory (EU) axiomatised by von Neumann and Morgenstern, Savage and others. This is less the case, however, in financial economics and mathematical finance, where investment decisions are commonly based on the methods of mean-variance (MV) introduced in the 1950s by Markowitz. Under the MV framework, each available investment opportunity (\"asset\") or portfolio is represented in just two dimensions by the ex ante mean and standard deviation $(\\mu,\\sigma)$ of the financial return anticipated from that investment. Utility adherents consider that in general MV methods are logically incoherent. Most famously, Norwegian insurance theorist Borch presented a proof suggesting that two-dimensional MV indifference curves cannot represent the preferences of a rational investor (he claimed that MV indifference curves \"do not exist\"). This is known as Borch\'s paradox and gave rise to an important but generally little-known philosophical literature relating MV to EU. We examine the main early contributions to this literature, focussing on Borch\'s logic and the arguments by which it has been set aside.
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