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. 2023 Jul;33(3):709-765.
doi: 10.1111/mafi.12376. Epub 2023 Jan 24.

Model-free portfolio theory: A rough path approach

Andrew L Allan  1 , Christa Cuchiero  2 , Chong Liu  3 , David J Prömel  4
Affiliations

Model-free portfolio theory: A rough path approach

Andrew L Allan et al. Math Financ. 2023 Jul.

Abstract

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.

Keywords: Cover's universal portfolio; log‐optimal portfolio; model uncertainty; pathwise integration; rough path; stochastic portfolio theory.

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Figures

FIGURE 1
FIGURE 1
Expected utility of the log‐optimal versus the alpha‐optimal portfolio over time [Colour figure can be viewed at wileyonlinelibrary.com]
See this image and copyright information in PMC

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