Based on a rough path foundation, we develop a model-free approach to stochastic portfolio theory (SPT). Our approach allows to handle significantly more general portfolios compared to previous model-free approaches based on Föllmer integration. Without the assumption of any underlying probabilistic model, we prove a pathwise formula for the relative wealth process, which reduces in the special case of functionally generated portfolios to a pathwise version of the so-called master formula of classical SPT. We show that the appropriately scaled asymptotic growth rate of a far reaching generalization of Cover's universal portfolio based on controlled paths coincides with that of the best retrospectively chosen portfolio within this class. We provide several novel results concerning rough integration, and highlight the advantages of the rough path approach by showing that (nonfunctionally generated) log-optimal portfolios in an ergodic Itô diffusion setting have the same asymptotic growth rate as Cover's universal portfolio and the best retrospectively chosen one.

中文翻译：

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无模型投资组合理论：粗略路径方法

基于粗略路径基础，我们开发了一种随机投资组合理论（SPT）的无模型方法。与之前基于 Föllmer 集成的无模型方法相比，我们的方法可以处理更通用的投资组合。在没有任何潜在概率模型的假设的情况下，我们证明了相对财富过程的路径公式，在函数生成投资组合的特殊情况下，该公式简化为所谓的经典 SPT 主公式的路径版本。我们证明，基于受控路径的 Cover 通用投资组合的深远概括的适当缩放的渐近增长率与此类中最佳回顾性选择的投资组合的渐进增长率一致。我们提供了一些关于粗集成的新颖结果，