Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-28T17:14:44.605Z Has data issue: false hasContentIssue false
  • English
  • Français

Superprophet inequalities for independent random variables

Part of: Stochastic processes Sequential methods

Published online by Cambridge University Press:  14 July 2016

Rainer Wittmann
Rainer Wittmann*
Affiliation:
Universität Göttingen
*
∗Postal address: Institut für Mathematische Stochastik, Universität Göttingen, Lotzestr. 13, D-37083 Göttingen, Germany.
Get access Rights & Permissions [Opens in a new window]

Abstract

As well as having complete knowledge of the future, a superprophet can also alter the order of observation as it is presented to a player without foresight, whose strategy is known to the prophet. It is shown that a superprophet can only do twice as well as his counterpart, if the underlying random sequence is independent.

Keywords

PROPHET INEQUALITIESOPTIMAL STOPPING

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 62L15: Optimal stopping
Type
Short Communications
Information
Journal of Applied Probability , Volume 33 , Issue 3 , September 1996 , pp. 904 - 908
Copyright
Copyright © Applied Probability Trust 1996 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Gilat, D. (1987) On the best order of observation in optimal stopping. J Appl. Prob. 24, 773–778.CrossRefGoogle Scholar
[2] Gnedin, A. V. and Krengel, U. (1995) A stochastic game of optimal stopping and order selection. Ann. Appl. Prob. 5, 310–321.Google Scholar
[3] Hill, T. P. (1983) Prophet inequalities and order selection in optimal stopping problems. Proc. Amer. Math. Soc. 88, 131–137.Google Scholar
[4] Hill, T. P. and Hordijk, A. (1985) Selection of order of observation in optimal stopping problems. J. Appl. Prob. 22, 177–184.Google Scholar
[5] Hill, T. P. and Kertz, R. P. (1982) Comparisons of stop rule and supremum expectations of i.i.d. random variables. Ann. Prob. 10, 336–345.Google Scholar
[6] Krengel, U. and Sucheston, L. (1978) On semiamarts, amarts and processes with finite values. Adv. Prob. 4, 197–266.Google Scholar
[7] Samuel-Cahn, E. (1984) Comparisons of threshold stop rules and maximum for independent non-negative random variables. Ann. Prob. 12, 1213–1216.Google Scholar
[8] Wittmann, R. (1995) Prophet inequalities for dependent random variables. Stochastics 52, 283–293.Google Scholar