Universal portfolios in continuous time: a model-free approach

2025-04-16

AI Summary

This paper addresses the existence and characterization of Cover’s universal portfolio in a continuous-time, model-free setting—without probabilistic assumptions. Methodologically, it employs Föllmer’s pathwise Itô calculus to establish, for the first time, the existence of a universal portfolio whose wealth process equals the pathwise average of all constant-rebalanced portfolios (CRPs). Using model-independent financial mathematics and self-financing strategy representations, the paper derives an explicit value formula for this portfolio and quantitatively relates CRP return differences to realized volatility. The key contribution is a rigorous, fully model-free existence proof and structural characterization of Cover’s universal portfolio in continuous time—breaking from traditional stochastic modeling paradigms. Results show that the universal portfolio dominates CRPs in terms of asymptotic growth while exhibiting lower realized volatility and variance, thereby providing a robust, pathwise foundation for universal investment strategies.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Sustainability of Web economics
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

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.

Problem

• Extends Cover's universal portfolios to continuous-time model-free settings
• Proves universal strategy's value equals average of constant rebalanced strategies
• Compares performance and volatility of constant rebalanced portfolios

Innovation

• Model-free pathwise Itô calculus approach
• Existence of universal portfolio strategy
• Comparison of self-financing trading strategies