英文标题：
《The geometry of relative arbitrage》
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作者：
Soumik Pal, Ting-Kam Leonard Wong
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最新提交年份：
2015
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英文摘要：
  Consider an equity market with $n$ stocks. The vector of proportions of the total market capitalizations that belong to each stock is called the market weight. The market weight defines the market portfolio which is a buy-and-hold portfolio representing the performance of the entire stock market. Consider a function that assigns a portfolio vector to each possible value of the market weight, and we perform self-financing trading using this portfolio function. We study the problem of characterizing functions such that the resulting portfolio will outperform the market portfolio in the long run under the conditions of diversity and sufficient volatility. No other assumption on the future behavior of stock prices is made. We prove that the only solutions are functionally generated portfolios in the sense of Fernholz. A second characterization is given as the optimal maps of a remarkable optimal transport problem. Both characterizations follow from a novel property of portfolios called multiplicative cyclical monotonicity.
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中文摘要：
考虑一个股票价值n美元的股票市场。每个股票的总市值比例向量称为市场权重。市场权重定义了市场投资组合，即代表整个股票市场表现的买入和持有投资组合。考虑一个函数，该函数为市场权重的每个可能值分配一个投资组合向量，我们使用该投资组合函数进行自筹资金交易。我们研究了在多样性和足够的波动性条件下，刻画函数的问题，使得最终的投资组合在长期内优于市场投资组合。没有对股票价格的未来行为做出其他假设。我们证明了唯一的解决方案是Fernholz意义下的函数生成投资组合。第二个特征是一个显著的最优运输问题的最优映射。这两个特征都源自投资组合的一个新特性，称为乘法循环单调性。
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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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