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On the best order of observation in optimal stopping problems

Published online by Cambridge University Press:  14 July 2016

David Gilat
David Gilat*
Affiliation:
Tel Aviv University
*
∗Postal address: School of Mathematical Sciences, Tel Aviv University, Ramat Aviv 69978, Israel.
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Abstract

For optimal stopping problems in which the player is allowed to choose the order of the random variables as well as the stopping rule, a notion of order equivalence is introduced. It is shown that different (non-degenerate) distributions cannot be order-equivalent.

This result unifies and generalizes two theorems of a similar nature recently obtained by Hill and Hordijk (1985).

Keywords

ORDER SELECTIONORDER EQUIVALENCE
Type
Short Communications
Information
Journal of Applied Probability , Volume 24 , Issue 3 , September 1987 , pp. 773 - 778
Copyright
Copyright © Applied Probability Trust 1987 

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References

Hill, T. P. (1983) Prophet inequalities and order selection in optimal stopping problems. Proc. Amer. Math. Soc. 88, 131–137.Google Scholar
Hill, T. P. and Hordijk, A. (1985) Selection of order of observation in optimal stopping problems. J. Appl. Prob. 22, 177–184.Google Scholar
Gilat, D. (1985) A prophet inequality with order selection for two independent random variables.Google Scholar