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A note on the full-information Poisson arrival selection problem

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Aiko Kurushima  and
Katsunori Ano
Aiko Kurushima*
Affiliation:
University of Tokyo
Katsunori Ano*
Affiliation:
Nanzan University
*
∗Postal address: Department of General Systems Studies, Graduate School of Arts and Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8902 Japan. Email address: [email protected]
∗∗Postal address: Department of Information Systems and Quantitative Sciences, Nanzan University, 18 Yamazato-cho, Showa-ku, Nagoya, 466-8673 Japan.
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Abstract

This note studies a Poisson arrival selection problem for the full-information case with an unknown intensity λ which has a Gamma prior density G(r, 1/a), where a>0 and r is a natural number. For the no-information case with the same setting, the problem is monotone and the one-step look-ahead rule is an optimal stopping rule; in contrast, this note proves that the full-information case is not a monotone stopping problem.

Keywords

Optimal stoppingsecretary problemOLA rulePoisson process

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 40 , Issue 4 , September 2003 , pp. 1147 - 1154
Copyright
Copyright © Applied Probability Trust 2003 

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