On Universal Portfolios with Continuous Side Information

TL;DR

This paper introduces a universal portfolio strategy that adapts to continuous side information, achieving asymptotic wealth guarantees comparable to the best state-constant rebalanced portfolio selected in hindsight, extending classical results.

Contribution

It extends universal portfolio theory to incorporate continuous side information and multiple state functions with finite Natarajan dimension, providing asymptotic wealth guarantees.

Findings

Achieves asymptotic wealth matching the best state-constant portfolio.

Extends classical universal portfolio results to continuous side information.

Provides theoretical guarantees for a broad class of state functions.

Abstract

A new portfolio selection strategy that adapts to a continuous side-information sequence is presented, with a universal wealth guarantee against a class of state-constant rebalanced portfolios with respect to a state function that maps each side-information symbol to a finite set of states. In particular, given that a state function belongs to a collection of functions of finite Natarajan dimension, the proposed strategy is shown to achieve, asymptotically to first order in the exponent, the same wealth as the best state-constant rebalanced portfolio with respect to the best state function, chosen in hindsight from observed market. This result can be viewed as an extension of the seminal work of Cover and Ordentlich (1996) that assumes a single state function.