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Selection of order of observation in optimal stopping problems

Published online by Cambridge University Press:  14 July 2016

Theodore P. Hill  and
Arie Hordijk
Theodore P. Hill*
Affiliation:
Georgia Institute of Technology
Arie Hordijk*
Affiliation:
University of Leiden
*
∗Postal address: School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA.
∗∗Postal address: Department of Mathematics, University of Leiden, Wassenaarseweg 80, Postbus 9512, 2300 Leiden, The Netherlands.
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Abstract

In optimal stopping problems in which the player is free to choose the order of observation of the random variables as well as the stopping rule, it is shown that in general there is no function of all the moments of individual integrable random variables, nor any function of the first n moments of uniformly bounded random variables, which can determine the optimal ordering. On the other hand, several fairly general rules for identification of the optimal ordering based on individual distributions are given, and applications are made to several special classes of distributions.

Keywords

ORDER SELECTIONOPTIMAL STOPPING THEORY
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 1 , March 1985 , pp. 177 - 184
Copyright
Copyright © Applied Probability Trust 1985 

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Footnotes

Research partially supported by a NATO Postdoctoral Fellowship.

References

Chow, Y. S., Robbins, H. and Siegmund, D. (1971) Great Expectations: The Theory of Optimal Stopping. Houghton Mifflin, Boston.Google Scholar
Feller, W. (1966) An Introduction to Probability Theory and its Applications, Vol. II. Wiley, New York.Google Scholar
Hill, T. P. (1983) Prophet inequalities and order selection in optimal stopping problems. Proc. Amer. Math. Soc. 88, 131–137.Google Scholar