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An approximate characterisation of optimal stopping boundaries

Published online by Cambridge University Press:  14 July 2016

P. Whittle
P. Whittle*
Affiliation:
University of Cambridge
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Abstract

An identity, of the type of Green's equation, is deduced for the loss function of a stopping process. This yields a set of relations determining the optimal (minimal loss) stopping boundary, which do not require simultaneous determination of the loss function in the stopping region. A no-overshoot approximation is invoked, but a bound on the magnitude of the terms neglected is obtained by appeal to a general version of Chernoff's tangency condition at an optimal boundary.

Keywords

OPTIMAL STOPPINGSEQUENTIAL ANALYSISGREEN'S EQUATION

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 1 , March 1973 , pp. 158 - 165
Copyright
Copyright © Applied Probability Trust 1973 

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References

[1] Chernoff, H. (1961) Sequential tests for the mean of a normal distribution. Proc. Fourth Berkeley Symposium on Math. Statist. and Prob. 1, 79–92. University of California Press, Berkeley.Google Scholar
[2] Whittle, P. (1964) Some general results in sequential analysis. Biometrika 51, 123–161.Google Scholar