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Log-Optimal Portfolio Selection Using the Blackwell Approachability Theorem

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  • Vladimir V'yugin

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.

Suggested Citation

  • Vladimir V'yugin, 2014. "Log-Optimal Portfolio Selection Using the Blackwell Approachability Theorem," Papers 1410.5996, arXiv.org, revised Jun 2015.
    • Handle: RePEc:arx:papers:1410.5996
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    References listed on IDEAS

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    1. Shie Mannor & Gilles Stoltz, 2009. "A Geometric Proof of Calibration," Working Papers hal-00442042, HAL.
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    3. Chen, Xiaohong & White, Halbert, 1996. "Laws of Large Numbers for Hilbert Space-Valued Mixingales with Applications," Econometric Theory, Cambridge University Press, vol. 12(2), pages 284-304, June.
    4. Shie Mannor & Gilles Stoltz, 2010. "A Geometric Proof of Calibration," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 721-727, November.
    5. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29, January.
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