Title

Prophet Inequalities for Parallel Processes

Author Info

Theodore P. Hill, Georgia Institute of Technology - Main CampusFollow
D. P. Kennedy, University of Cambridge

Recommended Citation

Postprint version. Published in Journal of Multivariate Analysis, Volume 31, Issue 3, November 1, 1989, pages 236-243.

Copyright © 1989 Elsevier.

NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.

The definitive version is available at https://doi.org/10.1016/0047-259X(89)90064-X.

Abstract

Generalizations of prophet inequalities for single sequences are obtained for optimal stopping of several parallel sequences of independent random variables. For example, if {X_{i, j}, 1 ≤ i ≤ n, 1 ≤ j < ∞} are independent non-negative random variables, then E(sup X_i,j) ≤ (n + 1) max sup {E(X_i,t): t is a stop rule for X_i,1, X_i,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