Universal portfolios in continuous time: an approach in pathwise Itô calculus

ArXiv ID: 2504.11881 “View on arXiv”

Authors: Unknown

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 Föllmer’s pathwise Itô 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 Itô calculus. We moreover provide a comparison result for the performance and the realized volatility and variance of constant rebalanced portfolio strategies.

Keywords: universal portfolio strategies, pathwise Itô calculus, constant rebalanced strategies, self-financing trading strategies, portfolio value process, Equities (Implied by portfolio strategies)

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 1.0/10
  • Quadrant: Lab Rats
  • Why: The paper is dense with advanced mathematical formalism, employing pathwise Itô calculus, functional analytic tools, and rigorous proofs of abstract theorems (e.g., equivalence of strategy descriptions, existence proofs), indicating high math complexity. However, it lacks any backtesting, empirical data analysis, or implementation details, focusing entirely on theoretical model-free construction without practical trading considerations, resulting in very low empirical rigor.
  flowchart TD
    A["Research Goal: Develop a continuous-time universal portfolio in a model-free setting"] --> B["Methodology: Pathwise Itô Calculus"]
    B --> C{"Comparison of Self-Financing Descriptions"}
    C --> D["Establish Universal Strategy Existence"]
    C --> E["Prove Portfolio Value = Average of Constant Rebalanced Strategies"]
    D --> F["Findings: Model-Free Performance & Volatility Comparison"]
    E --> F
    style A fill:#e1f5fe
    style F fill:#e8f5e8