The Annals of Probability

Sum the odds to one and stop

F. Thomas Bruss

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Abstract

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

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

Dates
First available: 18 April 2002

Permanent link to this document
http://projecteuclid.org/euclid.aop/1019160340

Mathematical Reviews number (MathSciNet)
MR1797879

Digital Object Identifier
doi:10.1214/aop/1019160340

Zentralblatt MATH identifier
1005.60055

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

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

Citation

Bruss, F. Thomas. Sum the odds to one and stop. The Annals of Probability 28 (2000), no. 3, 1384--1391. doi:10.1214/aop/1019160340. http://projecteuclid.org/euclid.aop/1019160340.


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References

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