Sum the odds to one and stop
Bruss, F. Thomas
Ann. Probab., Tome 28 (2000) no. 1, p. 1384-1391 / Harvested from Project Euclid
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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.
Publié le : 2000-06-14
Classification:  Optimal stopping,  stopping islands,  monotone case,  generating function,  arithmetic –geometric mean,  dice problems,  best choice,  speculation,  investment,  1/e-law.,  60G40 
@article{1019160340,
     author = {Bruss, F. Thomas},
     title = {Sum the odds to one and stop},
     journal = {Ann. Probab.},
     volume = {28},
     number = {1},
     year = {2000},
     pages = { 1384-1391},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1019160340}
}

Bruss, F. Thomas. Sum the odds to one and stop. Ann. Probab., Tome 28 (2000) no. 1, pp.  1384-1391. http://gdmltest.u-ga.fr/item/1019160340/