相对套利优化
Optimization of relative arbitrage
摘要：
在随机投资组合理论中，相对套利是一个股票投资组合，它保证在有限的时间内表现优于基准投资组合。当市场是多样化的和充分波动的，基准是市场或买入并持有的投资组合时，Fernholz引入的功能生成投资组合提供了一种构建相对套利的系统方法。在本文中，我们证明了，如果市场的投资组合被替换为平等或熵加权的投资组合等，没有相对套利可以构造在相同的条件下使用功能生成的投资组合。我们还介绍和研究了形状约束优化问题的功能生成的投资组合的最大似然估计的对数凹密度的精神。
英文摘要：
In stochastic portfolio theory, a relative arbitrage is an equity portfolio which is guaranteed to outperform a benchmark portfolio over a finite horizon. When the market is diverse and sufficiently volatile, and the benchmark is the market or a buy-and-hold portfolio, functionally generated portfolios introduced by Fernholz provide a systematic way of constructing relative arbitrages. In this paper we show that if the market portfolio is replaced by the equal or entropy weighted portfolio among many others, no relative arbitrages can be constructed under the same conditions using functionally generated portfolios. We also introduce and study a shaped-constrained optimization problem for functionally generated portfolios in the spirit of maximum likelihood estimation of a log-concave density.
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