RT Journal Article
T1 Phase transitions in optimal betting strategies
A1 Dinis Vizcaíno, Luis Ignacio
A1 Unterberger, J.
A1 Lacoste, D.
AB 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.
PB EPL Association, European Physical Society
SN 0295-5075
YR 2020
FD 2020-09
LK https://hdl.handle.net/20.500.14352/8295
UL https://hdl.handle.net/20.500.14352/8295
LA eng
NO 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.
NO Ministerio de Economía y Competitividad (MINECO)
DS Docta Complutense
RD 6 may 2025