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

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.