The Annals of Probability

Sum the odds to one and stop

F. Thomas Bruss

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The objective of this paper is to present two theorems which are directly applicable to optimal stopping problems involving independent indicator functions. The proofs are elementary. One implication of the results is a convenient solution algorithm to obtain the optimal stopping rule and the value.We will apply it to several examples of sequences of independent indicators, including sequences of random length. Another interesting implication of the results is that the well-known asymptotic value $1 / e$ for the classical best-choice problem is in fact a typical lower boundin a much more general class of problems.

Article information

Ann. Probab. Volume 28, Number 3 (2000), 1384-1391.

First available in Project Euclid: 18 April 2002

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Zentralblatt MATH identifier

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Optimal stopping stopping islands monotone case generating function arithmetic –geometric mean dice problems best choice speculation investment 1/e-law.


Bruss, F. Thomas. Sum the odds to one and stop. Ann. Probab. 28 (2000), no. 3, 1384--1391. doi:10.1214/aop/1019160340.

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