Log-Optimal Portfolio Selection Using the Blackwell Approachability Theorem

Preprint OPEN
Vladimir V'yugin (2014)
  • Subject: Quantitative Finance - Portfolio Management | Computer Science - Artificial Intelligence
    arxiv: Computer Science::Computational Engineering, Finance, and Science

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.
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