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oai:docta.ucm.es:20.500.14352/82952023-08-28T19:48:30Zcom_20.500.14352_14col_20.500.14352_15

00925njm 22002777a 4500 dc Dinis Vizcaíno, Luis Ignacio author Unterberger, J. author Lacoste, D. author 2020-09 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. 0295-5075 10.1209/0295-5075/131/60005 https://hdl.handle.net/20.500.14352/8295 https://doi.org/10.1209/0295-5075/131/60005 https://iopscience.iop.org/ Phase transitions in optimal betting strategies