Recommended Citation
Postprint version. Published in Journal of Multivariate Analysis, Volume 31, Issue 3, November 1, 1989, pages 236-243. Copyright © 1989 Elsevier. The definitive version is available at http://dx.doi.org/10.1016/0047-259X(89)90064-X.
NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.
Abstract
Generalizations of prophet inequalities for single sequences are obtained for optimal stopping of several parallel sequences of independent random variables. For example, if {Xi, j, 1 ≤ i ≤ n, 1 ≤ j < ∞} are independent non-negative random variables, then E(sup Xi,j) ≤ (n + 1) max sup {E(Xi,t): t is a stop rule for Xi,1, Xi,2, ...} and this bound is best possible. Applications are made to comparisons of the optimal expected returns of various alternative methods of stopping of parallel processes.
Disciplines
Mathematics
URL: http://digitalcommons.calpoly.edu/rgp_rsr/43