Model‐free portfolio theory: A rough path approach
基于粗糙路径理论，提出一种无模型的投资组合方法，无需假设概率模型即可推导相对财富过程路径公式，并证明Cover通用投资组合的推广形式与最优回顾投资组合具有相同渐近增长率。
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.