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On a stopping problem involving refusal and forced stopping

Published online by Cambridge University Press:  14 July 2016

Masami Yasuda
Masami Yasuda*
Affiliation:
Chiba University
*
∗ Postal address: College of General Education, Chiba University, Yayoi-cho, Chiba 260, Japan.
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Abstract

Although the usual optimal stopping problem is described as a Markov decision process with two decisions, stop and continue, we shall consider a model which distinguishes the observer's strategy from the system's two decisions. The observer can select a strategy defined on an action space, and the decision of the system to stop or continue is determined by a prescribed conditional probability. For this model, it may happen that the strategy (a) to stop is refused, or (b) to continue is forcibly stopped. This is a slight modification of the one-dimensional stopping problem by involving refusal and forced stopping. The model is motivated by the uncertain secretary choice problem of Smith (1975) and the multivariate stopping problem of Kurano, Yasuda and Nakagami (1980), (1982).

Keywords

OPTIMAL STOPPINGSECRETARY PROBLEMREFUSAL AND FORCED STOPPING
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 1 , March 1983 , pp. 71 - 81
Copyright
Copyright © Applied Probability Trust 1983 

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References

Bellman, R. (1957) Dynamic Programming. Princeton University Press.Google Scholar
Chow, Y. S., Robbins, H. and Siegmund, D. (1971) Great Expectations: The Theory of Optimal Stopping. Houghton Mifflin, Boston.Google Scholar
Kurano, M., Yasuda, M. and Nakagami, J. (1980) Multi-variate stopping problem with a majority rule. J. Operat. Res. Soc. Japan 23, 205–223.Google Scholar
Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden Day, San Francisco.Google Scholar
Smith, M. H. (1975) A secretary problem with uncertain employment. J. Appl. Prob. 12, 620–624.Google Scholar
Yasuda, M., Nakagami, N. and Kurano, M. (1982) Multi-variate stopping problems with a monotone rule. J. Operat. Res. Soc. Japan 25, 334–350.Google Scholar