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Moments of Random Sums and Robbins' Problem of Optimal Stopping

Published online by Cambridge University Press:  14 July 2016

Alexander Gnedin*
Affiliation:
Utrecht University
Alexander Iksanov*
Affiliation:
National Taras Shevchenko University of Kiev
*
Postal address: Department of Mathematics, Utrecht University, Postbus 80010, 3508 TA Utrecht, The Netherlands. Email address: a.v.gnedin@uu.nl
∗∗ Postal address: Faculty of Cybernetics, National Taras Shevchenko University of Kiev, Kiev 01033, Ukraine. Email address: iksan@univ.kiev.ua
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Abstract

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Robbins' problem of optimal stopping is that of minimising the expected rank of an observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the value of the stopped variable under the rule that yields the minimal expected rank, by embedding the problem in a much more general context of selection problems with the nonanticipation constraint lifted, and with the payoff growing like a power function of the rank.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 2011 

References

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