标题： 随机投资组合理论：机器学习视角 显示英文标题

标题： Stochastic Portfolio Theory: A Machine Learning Perspective

摘要： 在本文中，我们提出了一种高斯过程（GPs）在金融资产配置中的新应用。我们的方法深深植根于随机投资组合理论（SPT），这是一个由Robert Fernholz引入的随机分析框架，旨在灵活地分析股票市场中某些投资策略相对于基准指数的表现。特别是，SPT展示了一些基于公司规模的投资策略，在现实假设下，在某些时间范围内以概率1超越基准指数。受这一结果的激励，我们考虑了逆问题，即从历史数据中学习一个基于任何给定交易特征的最优投资策略，并使用用户指定的优化标准，该标准可能超越超越基准指数。尽管这个问题对投资管理从业者极为重要，但很难使用SPT框架来解决。我们表明，我们的机器学习方法学习到的投资策略在美股市场明显优于现有的SPT策略。 显示英文摘要

摘要： In this paper we propose a novel application of Gaussian processes (GPs) to financial asset allocation. Our approach is deeply rooted in Stochastic Portfolio Theory (SPT), a stochastic analysis framework introduced by Robert Fernholz that aims at flexibly analysing the performance of certain investment strategies in stock markets relative to benchmark indices. In particular, SPT has exhibited some investment strategies based on company sizes that, under realistic assumptions, outperform benchmark indices with probability 1 over certain time horizons. Galvanised by this result, we consider the inverse problem that consists of learning (from historical data) an optimal investment strategy based on any given set of trading characteristics, and using a user-specified optimality criterion that may go beyond outperforming a benchmark index. Although this inverse problem is of the utmost interest to investment management practitioners, it can hardly be tackled using the SPT framework. We show that our machine learning approach learns investment strategies that considerably outperform existing SPT strategies in the US stock market.