Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-05-22T12:38:57.262Z Has data issue: false hasContentIssue false
  • English
  • Français

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: kul@rr.iij4u.or.jp
∗∗Postal address: Department of Information Systems and Quantitative Sciences, Nanzan University, 18 Yamazato-cho, Showa-ku, Nagoya, 466-8673 Japan.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ano, K. (2000). Mathematics of Timing—-Optimal Stopping Problem. Asakura, Tokyo (in Japanese).Google Scholar
Ano, K. (2001). Multiple selection problem and OLA stopping rule. Sci. Math. Japon. 53, 335–346.Google Scholar
Ano, K., and Ando, M. (2000). A note on Bruss' stopping problem with random availability. In Game Theory, Optimal Stopping, Probability and Statistics (IMS Lecture Notes Monogr. Ser. 35), eds. Bruss, F. T. and Le Cam, L., Institute of Mathematical Statistics, Beachwood, OH, pp. 71–82.Google Scholar
Bruss, F. T. (1987). On an optimal selection problem by Cowan and Zabczyk. J. Appl. Prob. 24, 918–928.Google Scholar
Bruss, F. T. (2000). Sum the odds to one and stop. Ann. Prob. 28, 1384–1391.Google Scholar
Bruss, F. T., and Paindaveine, D. (2000). Selecting a sequence of last successes in independent trials. J. Appl. Prob. 37, 389–399.Google Scholar
Chow, Y. S., Robbins, H., and Siegmund, D. (1971). Great Expectations: The Theory of Optimal Stopping. Houghton Mifflin, Boston, MA.Google Scholar
Cowan, R., and Zabczyk, J. (1978). An optimal selection problem associated with the Poisson process. Theory Prob. Appl. 23, 584–592.CrossRefGoogle Scholar
Kurushima, A., and Ano, K. (2003). A Poisson arrival selection problem for Gamma prior intensity with natural number parameter. Sci. Math. Japon. 57, 217–231.Google Scholar
Sakaguchi, M. (1989). Some infinite problems in classical secretary problems. Math. Japon. 34, 307–318.Google Scholar