Log-Optimal Portfolio Selection Using the Blackwell Approachability Theorem

TL;DR

This paper introduces a novel method for constructing log-optimal portfolios using well-calibrated market forecasts based on the Blackwell approachability theorem, avoiding stochastic assumptions about market behavior.

Contribution

It combines calibration techniques with the Blackwell approachability theorem to develop a portfolio selection method that guarantees asymptotic performance without stochastic market assumptions.

Findings

Portfolio performs at least as well as any stationary portfolio asymptotically.

Uses well-calibrated forecasts derived from the Blackwell approachability theorem.

No stochastic assumptions are required about market values.

Abstract

We present a method for constructing the log-optimal portfolio using the well-calibrated forecasts of market values. Dawid's notion of calibration and the Blackwell approachability theorem are used for computing well-calibrated forecasts. We select a portfolio using this "artificial" probability distribution of market values. Our portfolio performs asymptotically at least as well as any stationary portfolio that redistributes the investment at each round using a continuous function of side information. Unlike in classical mathematical finance theory, no stochastic assumptions are made about market values.