Log-Optimal Portfolio Selection Using the Blackwell Approachability Theorem
This provides a non-stochastic framework for portfolio optimization, which is incremental as it adapts existing calibration and approachability methods to finance.
The paper tackles the problem of log-optimal portfolio selection without stochastic assumptions by using well-calibrated forecasts derived from the Blackwell approachability theorem, resulting in a portfolio that asymptotically performs at least as well as any stationary portfolio based on continuous functions of side information.
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.