英文标题：
《Volatility and Arbitrage》
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作者：
E. Robert Fernholz, Ioannis Karatzas, Johannes Ruf
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最新提交年份：
2016
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英文摘要：
  The capitalization-weighted total relative variation $\\sum_{i=1}^d \\int_0^\\cdot \\mu_i (t) \\mathrm{d} \\langle \\log \\mu_i \\rangle (t)$ in an equity market consisting of a fixed number $d$ of assets with capitalization weights $\\mu_i (\\cdot)$ is an observable and nondecreasing function of time. If this observable of the market is not just nondecreasing, but actually grows at a rate which is bounded away from zero, then strong arbitrage can be constructed relative to the market over sufficiently long time horizons. It has been an open issue for more than ten years, whether such strong outperformance of the market is possible also over arbitrary time horizons under the stated condition. We show that this is not possible in general, thus settling this long-open question. We also show that, under appropriate additional conditions, outperformance over any time horizon indeed becomes possible, and exhibit investment strategies that effect it.
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中文摘要：
资本化加权总相对变化$\\sum\\ui=1}^d\\int\\u 0 ^\\cdot\\mu\\u i（t）\\mathrm{d}\\langle\\log\\mu\\u i\\rangle（t）$在由固定数量的资产组成的股票市场中，资本化权重$\\mu\\u i（\\cdot）$是一个可观察且不减损的时间函数。如果市场的这种可观察性不仅是非减损的，而且实际上是以远离零的速度增长的，那么就可以在足够长的时间范围内构建相对于市场的强套利。十多年来一直是一个悬而未决的问题，在规定的条件下，在任意的时间范围内，市场是否也可能表现出如此强劲的表现。我们表明，这在一般情况下是不可能的，从而解决了这个长期悬而未决的问题。我们还表明，在适当的附加条件下，在任何时间范围内都有可能实现跑赢大市，并展示了影响跑赢大市的投资策略。
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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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一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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