## Journal of Applied Probability

### The Kelly system maximizes median fortune

S. N. Ethier

#### 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.

#### Article information

Source
J. Appl. Probab. Volume 41, Number 4 (2004), 1230-1236.

Dates
First available in Project Euclid: 30 November 2004

https://projecteuclid.org/euclid.jap/1101840570

Digital Object Identifier
doi:10.1239/jap/1101840570

Mathematical Reviews number (MathSciNet)
MR2122819

Zentralblatt MATH identifier
1062.60045

#### Citation

Ethier, S. N. The Kelly system maximizes median fortune. J. Appl. Probab. 41 (2004), no. 4, 1230--1236. doi:10.1239/jap/1101840570. https://projecteuclid.org/euclid.jap/1101840570

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