Volume 131, Number 6, September 2020
|Number of page(s)||7|
|Published online||03 November 2020|
Phase transitions in optimal betting strategies
1 GISC - Grupo Interdisciplinar de Sistemas Complejos and Dpto. de Estructura de la Materia, Física Térmica y Electrónica, Universidad Complutense de Madrid - E-28040 Madrid, Spain
2 Institut Elie Cartan, UMR CNRS 7502, Université de Lorraine - BP 239, F-54506 Vandoeuvre- lès-Nancy Cedex, France
3 Gulliver Laboratory, UMR CNRS 7083, PSL Research University, ESPCI - 10 rue Vauquelin, F-75231 Paris Cedex 05, France
Received: 18 May 2020
Accepted: 23 September 2020
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.
PACS: 05.70.Ln – Nonequilibrium and irreversible thermodynamics / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 02.50.Le – Decision theory and game theory
© 2020 EPLA
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.