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The geometry of relative arbitrage

机译：相对套利的几何

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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.
机译：考虑一个有n只股票的股票市场。属于每只股票的总市值比例的向量称为市场权重。市场权重定义了市场投资组合，它是代表整个股票市场表现的买入和持有投资组合。考虑一个为市场权重的每个可能值分配投资组合向量的函数，我们使用该投资组合函数执行自筹资金交易。我们研究了表征功能的问题，以便在多样性和足够动荡的情况下，最终的投资组合从长远来看将超过市场组合。没有对股票价格的未来行为做出其他假设。我们证明，唯一的解决方案是Fernholz所说的功能生成的产品组合。第二个特征是显着的最优运输问题的最优映射。这两个特征都来自被称为乘性循环单调性的投资组合的一种新颖性质。

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