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arXiv · 2504.11881

Universal portfolios in continuous time: an approach in pathwise It\^o calculus

Xiyue Han·Alexander Schied
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Abstract

We provide a simple and straightforward approach to a continuous-time version of Cover's universal portfolio strategies within the model-free context of F\"ollmer's pathwise It\^o calculus. We establish the existence of the universal portfolio strategy and prove that its portfolio value process is the average of all values of constant rebalanced strategies. This result relies on a systematic comparison between two alternative descriptions of self-financing trading strategies within pathwise It\^o calculus. We moreover provide a comparison result for the performance and the realized volatility and variance of constant rebalanced portfolio strategies.

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Xiyue Han, Alexander Schied. 2025-04-16. Universal portfolios in continuous time: an approach in pathwise It\^o calculus. https://arxiv.org/abs/2504.11881

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