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Universal portfolios in continuous time: a model-free approach

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  • Xiyue Han
  • Alexander Schied

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. "Universal portfolios in continuous time: a model-free approach," Papers 2504.11881, arXiv.org.
    • Handle: RePEc:arx:papers:2504.11881
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    File URL: http://arxiv.org/pdf/2504.11881
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