Journal of Applied Probability

Moments of random sums and Robbins' problem of optimal stopping

Alexander Gnedin and Alexander Iksanov

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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.

Article information

J. Appl. Probab., Volume 48, Number 4 (2011), 1197-1199.

First available in Project Euclid: 16 December 2011

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60G50: Sums of independent random variables; random walks

Stopping time Robbins' problem of minimising the expected rank Poisson embedding random sum


Gnedin, Alexander; Iksanov, Alexander. Moments of random sums and Robbins' problem of optimal stopping. J. Appl. Probab. 48 (2011), no. 4, 1197--1199. doi:10.1239/jap/1324046028.

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