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arXiv · 1107.3315

Moments of random sums and Robbins' problem of optimal stopping

Alexander Gnedin·Alexander Iksanov
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Abstract

Robbins' problem of optimal stopping asks one to minimise the expected {\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\it value} of the stopped variable under the rule optimal in the sense of the 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.

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Alexander Gnedin, Alexander Iksanov. 2011-07-17. Moments of random sums and Robbins' problem of optimal stopping. https://doi.org/10.1239/jap/1324046028

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