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Superprophet inequalities for independent random variables

Part of:Stochastic processesSequential 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.
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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

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 33 , Issue 3 , September 1996, pp. 904 - 908
Copyright
Copyright © Applied Probability Trust 1996 

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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