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Moments of Random Sums and Robbins' Problem of Optimal Stopping

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Alexander Gnedin  and
Alexander Iksanov
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.

Keywords

Stopping timeRobbins' problem of minimising the expected rankPoisson embeddingrandom sum

MSC classification

Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory 60G50: Sums of independent random variables; random walks
Type
Short Communications
Information
Journal of Applied Probability , Volume 48 , Issue 4 , December 2011 , pp. 1197 - 1199
Copyright
Copyright © Applied Probability Trust 2011 

References

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