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Model‐free portfolio theory: A rough path approach

Allan, Andrew L.; Cuchiero, Christa; Liu, Chong; Prömel, David J.

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Christa Cuchiero

Chong Liu

David J. Prömel


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.


Allan, A. L., Cuchiero, C., Liu, C., & Prömel, D. J. (2023). Model‐free portfolio theory: A rough path approach. Mathematical Finance, 33(3), 709-765.

Journal Article Type Article
Acceptance Date Dec 21, 2022
Online Publication Date Jan 24, 2023
Publication Date 2023-07
Deposit Date Jan 24, 2023
Publicly Available Date Jun 30, 2023
Journal Mathematical Finance
Print ISSN 0960-1627
Electronic ISSN 1467-9965
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 33
Issue 3
Pages 709-765


Published Journal Article (729 Kb)

Publisher Licence URL

Copyright Statement
&copy; 2023 The Authors. Mathematical Finance published by Wiley Periodicals LLC.<br /> <br /> This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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