Abstract
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.
Citation
Alexander Gnedin. Alexander Iksanov. "Moments of random sums and Robbins' problem of optimal stopping." J. Appl. Probab. 48 (4) 1197 - 1199, December 2011. https://doi.org/10.1239/jap/1324046028
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