Open Access
Translator Disclaimer
July 2000 Sum the odds to one and stop
F. Thomas Bruss
Ann. Probab. 28(3): 1384-1391 (July 2000). DOI: 10.1214/aop/1019160340


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.


Download Citation

F. Thomas Bruss. "Sum the odds to one and stop." Ann. Probab. 28 (3) 1384 - 1391, July 2000.


Published: July 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1005.60055
MathSciNet: MR1797879
Digital Object Identifier: 10.1214/aop/1019160340

Primary: 60G40

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

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.28 • No. 3 • July 2000
Back to Top