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The trade-off between growth and risk in Kelly’s gambling and beyond

Author

Listed:
  • Cavallero, S.
  • Rousselot, A.
  • Pugatch, R.
  • Dinis, L.
  • Lacoste, D.

Abstract

We study a generalization of Kelly’s horse model to situations where gambling on horses other than the winning horse does not lead to a complete loss of the investment. In such cases, the odds matrix is non-diagonal, which is particularly interesting for biological applications. We examine the trade-off between the mean growth rate and its asymptotic variance, an approximation for risk. Because the consequences of fluctuations around the average growth rate are asymmetric, we further explore a better alternative definition of risk: the extinction probability and its implications for Kelly gambling and the risk-return trade-off. We discuss some applications of these concepts in biology and ecology.

Suggested Citation

  • Cavallero, S. & Rousselot, A. & Pugatch, R. & Dinis, L. & Lacoste, D., 2025. "The trade-off between growth and risk in Kelly’s gambling and beyond," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 659(C).
    • Handle: RePEc:eee:phsmap:v:659:y:2025:i:c:s0378437124008264
    DOI: 10.1016/j.physa.2024.130316
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    References listed on IDEAS

    as
    1. Enzo Busseti & Ernest K. Ryu & Stephen Boyd, 2016. "Risk-Constrained Kelly Gambling," Papers 1603.06183, arXiv.org.
    2. Maslov, Sergei & Zhang, Yi-Cheng, 1999. "Probability distribution of drawdowns in risky investments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 262(1), pages 232-241.
    3. Satya Majumdar & Jean-Philippe Bouchaud, 2008. "Optimal time to sell a stock in the Black-Scholes model: comment on 'Thou shalt buy and hold', by A. Shiryaev, Z. Xu and X.Y. Zhou," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 753-760.
    4. Anton V. Proskurnikov & B. Ross Barmish, 2023. "On the Benefit of Nonlinear Control for Robust Logarithmic Growth: Coin Flipping Games as a Demonstration Case," Papers 2303.10417, arXiv.org, revised May 2023.
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