Model-free portfolio theory: A rough path approach
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, and show that the appropriately scaled asymptotic growth rate of a generalization of Cover’s universal portfolio based on controlled paths coincides with that of the best retrospectively chosen portfolio within this class.
Andy completed his DPhil at Oxford University in 2019 under the supervision of Sam Cohen. He was then a postdoc in the Stochastic Finance group at ETH Zurich, and recently started as an Assistant Professor in Probability at Durham University.
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