Journal of Applied Probability

Moments of random sums and Robbins' problem of optimal stopping

Alexander Gnedin and Alexander Iksanov

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
J. Appl. Probab., Volume 48, Number 4 (2011), 1197-1199.

Dates
First available in Project Euclid: 16 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1324046028

Digital Object Identifier
doi:10.1239/jap/1324046028

Mathematical Reviews number (MathSciNet)
MR2896677

Zentralblatt MATH identifier
1250.62041

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60G50: Sums of independent random variables; random walks

Keywords
Stopping time Robbins' problem of minimising the expected rank Poisson embedding random sum

Citation

Gnedin, Alexander; Iksanov, Alexander. Moments of random sums and Robbins' problem of optimal stopping. J. Appl. Probab. 48 (2011), no. 4, 1197--1199. doi:10.1239/jap/1324046028. https://projecteuclid.org/euclid.jap/1324046028


Export citation