Maximizing expected value with two stage stopping rules

David Assaf, Larry Goldstein and Ester Samuel-Cahn

Discussion Paper Series from The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem

Abstract: Let X n ,…,X 1 be i.i.d. random variables with distribution function F and finite expectation. A statistician, knowing F, observes the X values sequentially and is given two chances to choose X's using stopping rules. The statistician's goal is to select a value of X as large as possible. Let V n 2 equal the expectation of the larger of the two values chosen by the statistician when proceeding optimally. We obtain the asymptotic behavior of the sequence V n 2 for a large class of F's belonging to the domain of attraction (for the maximum) D(G II ? ), where G II ? (x) = exp(-x -? )I(x > 0) with ? > 1. The results are compared with those for the asymptotic behavior of the classical one choice value sequence V n 1 , as well as with the "prophet value" sequence E(max{X n ,…,X 1 }), and indicate that substantial improvement is obtained when given two chances to stop, rather than one.

Keywords: multiple choice stopping rules; domains of attraction; prophet value Classification-MSC-2000: 60G40 (search for similar items in EconPapers)
Pages: 21 pages
Date: 2004-03
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Published in Random Walks, Sequential Analysis and Related Topics, Chao Agnes Hsiung, Zhiliang Ying and Cun-Hui Zhang, Eds. World Scientific, Singapore (2006), pp. 3-27.

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