Moments of Random Sums and Robbins' Problem of Optimal Stopping
ALEXANDER V. GNEDIN, Alexander Iksanov · Journal of Applied Probability · 2011
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.