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Two theorems on optimal stopping with backward solicitation

Published online by Cambridge University Press:  14 July 2016

Edi Karni  and
Aba Schwartz
Edi Karni
Affiliation:
Tel-Aviv University
Aba Schwartz
Affiliation:
Tel-Aviv University
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Abstract

This paper deals with optimal stopping rules for a sampling process with uncertain recall, i.e. the probability that a past observation is currently available declines exponentially with the time elapsed since it was last observed. The main result of this paper is that for such sampling processes, and for any utility function, if a solicitation of a past observation incurs the same cost as a new draw, then it is never optimal to continue the sampling when the observation solicited is found to be available. This result applies to both bounded and unbounded sequential decision procedures.

Keywords

OPTIMAL STOPPINGSAMPLING WITH UNCERTAIN RECALLSTOCHASTICALLY INDEPENDENT BACKWARD SOLICITATION

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 14 , Issue 4 , December 1977 , pp. 869 - 875
Copyright
Copyright © Applied Probability Trust 1977 

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References

[1] DeGroot, M. H. (1970) Optimal Statistical Decisions McGraw-Hill, New York.Google Scholar
[2] Yang, M. C. K. (1974) Recognizing the maximum of a random sequence based on relative rank with backward solicitation. J. Appl. Prob. 11, 504–512.Google Scholar