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Weber’s optimal stopping problem and generalizations

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  • Dendievel, Rémi

Abstract

One way to interpret the classical secretary problem (CSP) is to consider it as a special case of the following problem. We observe n independent indicator variables I1,I2,…,In sequentially and we try to stop on the last variable being equal to 1. If Ik=1 it means that the kth observed secretary has smaller rank than all previous ones (and therefore is a better secretary). In the CSP, pk=E(Ik)=1/k and the last k with Ik=1 stands for the best candidate. The more general problem of stopping on a last “1” was studied by Bruss (2000). In what we will call Weber’s problem the indicators are replaced by random variables which can take more than 2 values. The goal is now to maximize the probability of stopping on a value appearing for the last time in the sequence. Notice that we do not fix in advance the value taken by the variable on which we stop.

Suggested Citation

  • Dendievel, Rémi, 2015. "Weber’s optimal stopping problem and generalizations," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 176-184.
    • Handle: RePEc:eee:stapro:v:97:y:2015:i:c:p:176-184
    DOI: 10.1016/j.spl.2014.11.002
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    References listed on IDEAS

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    1. Bruss, F. Thomas & Paindaveine, Davy, 2000. "Selecting a sequence of last successes in independent trials," MPRA Paper 21166, University Library of Munich, Germany.
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