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Optimality of myopic stopping times for geometric discounting

Published online by Cambridge University Press:  14 July 2016

Bert Fristedt  and
Donald A. Berry
Bert Fristedt*
Affiliation:
University of Minnesota
Donald A. Berry*
Affiliation:
University of Minnesota
*
∗ Postal address: School of Mathematics, 127 Vincent Hall, 206 Church Street SE, University of Minnesota, Minneapolis, MN 55455, USA.
∗∗ Postal address: Department of Theoretical Statistics, 270 Vincent Hall, 206 Church Street SE, University of Minnesota, Minneapolis, MN 55455, USA.
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Abstract

Consider a sequence of conditionally independent Bernoulli random variables taking on the values 1 and − 1. The objective is to stop the sequence in order to maximize the discounted sum. Suppose the Bernoulli parameter has a beta distribution with integral parameters. It is optimal to stop when the conditional expectation of the next random variable is negative provided the discount factor is less than or equal to . Moreover, is best possible. The case where the parameters of the beta distribution are arbitrary positive numbers is also treated.

Keywords

GAMBLINGBANDIT PROBLEMFUNDAMENTAL THEOREM OF GAMBLINGBETA DISTRIBUTIONS

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 25 , Issue 2 , June 1988 , pp. 437 - 443
Copyright
Copyright © Applied Probability Trust 1988 

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Footnotes

Research partially supported by NSF grant DMS 86–03437.

Research partially supported by NSF grant DMS 85–05023.

References

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