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An optimal betting strategy for repeated games

Published online by Cambridge University Press:  14 July 2016

Gary Gottlieb
Gary Gottlieb*
Affiliation:
New York University
*
∗ Postal address: Department of Quantitative Analysis, College of Business and Public Administration, New York University, Washington Square, New York, NY 10003, USA.
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Abstract

We consider the problem of finding a betting strategy for an infinite sequence of wagers where the optimality criterion is the minimization of the expected exit time of wealth from an interval. We add the side constraint that the right boundary is hit first with at least some specified probability. The optimal strategy is derived for a diffusion approximation.

Keywords

GAMBLING SYSTEMSKELLY CRITERIAOPTIMALITY CRITERIADIFFUSION APPROXIMATIONREPEATED GAMES
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 4 , December 1985 , pp. 787 - 795
Copyright
Copyright © Applied Probability Trust 1985 

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