Moments of random sums and Robbins' problem of optimal stopping

Details Moments of random sums and Robbins' problem of optimal stopping Moments of random sums and Robbins' problem of optimal stopping

2011-07-17

arxiv.org/abs/1107.3315v1

Mathematics

Probability

Scientific paper

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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