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Diversification and limited information in the Kelly game

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  • Matus Medo
  • Yury M. Pis'mak
  • Yi-Cheng Zhang

Abstract

Financial markets, with their vast range of different investment opportunities, can be seen as a system of many different simultaneous games with diverse and often unknown levels of risk and reward. We introduce generalizations to the classic Kelly investment game [Kelly (1956)] that incorporates these features, and use them to investigate the influence of diversification and limited information on Kelly-optimal portfolios. In particular we present approximate formulas for optimizing diversified portfolios and exact results for optimal investment in unknown games where the only available information is past outcomes.

Suggested Citation

  • Matus Medo & Yury M. Pis'mak & Yi-Cheng Zhang, 2008. "Diversification and limited information in the Kelly game," Papers 0803.1364, arXiv.org, revised Jul 2008.
    • Handle: RePEc:arx:papers:0803.1364
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    Cited by:

    1. Matus Medo & Chi Ho Yeung & Yi-Cheng Zhang, 2008. "How to quantify the influence of correlations on investment diversification," Papers 0805.3397, arXiv.org, revised Feb 2009.
    2. Paolo Laureti & Matus Medo & Yi-Cheng Zhang, 2010. "Analysis of Kelly-optimal portfolios," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 689-697.
    3. Jan Lorenz & Fabian Paetzel & Frank Schweitzer, 2013. "Redistribution Spurs Growth by Using a Portfolio Effect on Risky Human Capital," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-13, February.
    4. Luo Yong & Zhu Bo & Tang Yong, 2015. "Dynamic optimal capital growth of diversified investment," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(3), pages 577-588, March.
    5. Rose D. Baker & Ian G. McHale, 2013. "Optimal Betting Under Parameter Uncertainty: Improving the Kelly Criterion," Decision Analysis, INFORMS, vol. 10(3), pages 189-199, September.
    6. Medo, Matús & Yeung, Chi Ho & Zhang, Yi-Cheng, 2009. "How to quantify the influence of correlations on investment diversification," International Review of Financial Analysis, Elsevier, vol. 18(1-2), pages 34-39, March.
    7. Joseph B. Kadane, 2011. "Partial-Kelly Strategies and Expected Utility: Small-Edge Asymptotics," Decision Analysis, INFORMS, vol. 8(1), pages 4-9, March.

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