Moments of Random Sums and Robbins' Problem of Optimal Stopping

Abstract

Robbins' problem of optimal stopping is that of minimising the expectedrankof an observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding thevalueof 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.