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A New Interpretation of Information Rate

In: THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE

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  • J. L. KELLY JR.

Abstract

If the input symbols to a communication channel represent the outcomes of a chance event on which bets are available at odds consistent with their probabilities (i.e., “fair” odds), a gambler can use the knowledge given him by the received symbols to cause his money to grow exponentially. The maximum exponential rate of growth of the gambler's capital is equal to the rate of transmission of information over the channel. This result is generalized to include the case of arbitrary odds.Thus we find a situation in which the transmission rate is significant even though no coding is contemplated. Previously this quantity was given significance only by a theorem of Shannon's which asserted that, with suitable encoding, binary digits could be transmitted over the channel at this rate with an arbitrarily small probability of error.

Suggested Citation

  • J. L. Kelly Jr., 2011. "A New Interpretation of Information Rate," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 3, pages 25-34, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814293501_0003
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    Cited by:

    1. Didier Sornette & Spencer Wheatley & Peter Cauwels, 2019. "The fair reward problem: the illusion of success and how to solve it," Papers 1902.04940, arXiv.org, revised Apr 2019.
    2. Paula Villa Martín & Miguel A Muñoz & Simone Pigolotti, 2019. "Bet-hedging strategies in expanding populations," PLOS Computational Biology, Public Library of Science, vol. 15(4), pages 1-17, April.
    3. A. Ferrer-Sapena & J. M. Calabuig & L. M. García Raffi & E. A. Sánchez Pérez, 2020. "Where Should I Submit My Work for Publication? An Asymmetrical Classification Model to Optimize Choice," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 490-508, July.
    4. Liu Ziyin & Kentaro Minami & Kentaro Imajo, 2021. "Theoretically Motivated Data Augmentation and Regularization for Portfolio Construction," Papers 2106.04114, arXiv.org, revised Dec 2022.
    5. da Costa, Igor Barbosa & Marinho, Leandro Balby & Pires, Carlos Eduardo Santos, 2022. "Forecasting football results and exploiting betting markets: The case of “both teams to score”," International Journal of Forecasting, Elsevier, vol. 38(3), pages 895-909.
    6. Vladimir Petrov & Anton Golub & Richard Olsen, 2019. "Instantaneous Volatility Seasonality of High-Frequency Markets in Directional-Change Intrinsic Time," JRFM, MDPI, vol. 12(2), pages 1-31, April.
    7. Mu-En Wu & Jia-Hao Syu & Chien-Ming Chen, 2022. "Kelly-Based Options Trading Strategies on Settlement Date via Supervised Learning Algorithms," Computational Economics, Springer;Society for Computational Economics, vol. 59(4), pages 1627-1644, April.

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