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摘要翻译：
如果一个金融市场不允许单一股票在相对资本化方面主宰整个市场，那么这个市场就被称为“多样化”。在Samuelson(1965)提出的标准Ito过程模型的背景下，我们用精确的术语表述了这个性质（以及相关的、相继较弱的“弱多样性”和“渐近弱多样性”的概念）。我们表明多样性是可能实现的，但很微妙。提供了几个说明性的例子，这些例子表明弱多样性金融市场包含相对套利机会：在足够长的时间范围内有可能超过（或低于）这种市场，在任意的时间范围内有可能显著低于它们。这种相对套利的存在并不影响期权定价的发展，而且对长期权证的定价和看跌平价的定价产生了有趣的影响。提出了几个有待进一步研究的问题。
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英文标题：
《Diversity and relative arbitrage in equity markets》
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作者：
Robert Fernholz, Ioannis Karatzas, Constantinos Kardaras
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最新提交年份：
2008
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
A financial market is called "diverse" if no single stock is ever allowed to dominate the entire market in terms of relative capitalization. In the context of the standard Ito-process model initiated by Samuelson (1965) we formulate this property (and the allied, successively weaker notions of "weak diversity" and "asymptotic weak diversity") in precise terms. We show that diversity is possible to achieve, but delicate. Several illustrative examples are provided, which demonstrate that weakly-diverse financial markets contain relative arbitrage opportunities: it is possible to outperform (or underperform) such markets over sufficiently long time-horizons, and to underperform them significantly over arbitrary time-horizons. The existence of such relative arbitrage does not interfere with the development of option pricing, and has interesting consequences for the pricing of long-term warrants and for put-call parity. Several open questions are suggested for further study.
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PDF链接：
https://arxiv.org/pdf/0803.3093
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