Open Access
Translator Disclaimer
May, 1992 Sharp Inequalities for Optimal Stopping with Rewards Based on Ranks
T. P. Hill, D. P. Kennedy
Ann. Appl. Probab. 2(2): 503-517 (May, 1992). DOI: 10.1214/aoap/1177005713


A universal bound for the maximal expected reward is obtained for stopping a sequence of independent random variables where the reward is a nonincreasing function of the rank of the variable selected. This bound is shown to be sharp in three classical cases: (i) when maximizing the probability of choosing one of the $k$ best; (ii) when minimizing the expected rank; and (iii) for an exponential function of the rank.


Download Citation

T. P. Hill. D. P. Kennedy. "Sharp Inequalities for Optimal Stopping with Rewards Based on Ranks." Ann. Appl. Probab. 2 (2) 503 - 517, May, 1992.


Published: May, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0758.60041
MathSciNet: MR1161064
Digital Object Identifier: 10.1214/aoap/1177005713

Primary: 60G40

Keywords: best choice problem , Optimal stopping , prophet inequality , ‎rank‎ , Schur convexity , secretary problem , sharp inequalities

Rights: Copyright © 1992 Institute of Mathematical Statistics


Vol.2 • No. 2 • May, 1992
Back to Top