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The Kelly system maximizes median fortune

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

S. N. Ethier
S. N. Ethier*
Affiliation:
University of Utah
*
∗ Postal address: Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA. Email address: ethier@math.utah.edu
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Abstract

It is well known that the Kelly system of proportional betting, which maximizes the long-term geometric rate of growth of the gambler's fortune, minimizes the expected time required to reach a specified goal. Less well known is the fact that it maximizes the median of the gambler's fortune. This was pointed out by the author in a 1988 paper, but only under asymptotic assumptions that might cause one to question its applicability. Here we show that the result is true more generally, and argue that this is a desirable property of the Kelly system.

Keywords

Gamblingoptimal proportional betting

MSC classification

Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 41 , Issue 4 , December 2004 , pp. 1230 - 1236
Copyright
Copyright © Applied Probability Trust 2004 

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