Phase transitions in optimal betting strategies



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Dinis Vizcaíno, Luis Ignacio and Unterberger, J. and Lacoste, D. (2020) Phase transitions in optimal betting strategies. EPL, 131 (6). ISSN 0295-5075

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Kelly's criterion is a betting strategy that maximizes the long-term growth rate, but which is known to be risky. Here, we find optimal betting strategies that gives the highest capital growth rate while keeping a certain low value of risky fluctuations. We then analyze the trade-off between the average and the fluctuations of the growth rate, in models of horse races, first for two horses then for an arbitrary number of horses, and for uncorrelated or correlated races. We find an analog of a phase transition with a coexistence between two optimal strategies, where one has risk and the other one does not. The above trade-off is also embodied in a general bound on the average growth rate, similar to thermodynamic uncertainty relations. We also prove mathematically the absence of other phase transitions between Kelly's point and the risk-free strategy.

Item Type:Article
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Copyright © 2020 EPLA. LD acknowledges financial support from Spanish Ministerio de Economia, Industria y Competitividad through grant FIS2017-83709-R. We acknowledge many insightful discussions with L. Peliti and E. Aurell.

Uncontrolled Keywords:Physics, Multidisciplinary
Subjects:Sciences > Physics > Nuclear physics
ID Code:66820
Deposited On:28 Jul 2021 07:47
Last Modified:19 Aug 2021 07:10

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