Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-14T13:24:25.311Z Has data issue: false hasContentIssue false
  • English
  • Français

On the full information best-choice problem

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Alexander V. Gnedin
Alexander V. Gnedin*
Affiliation:
Universität Göttingen
*
∗Postal address: Institut für Mathematische Stochastik, Universität Göttingen, Lotzestr. 13, D-37083 Göttingen, Germany.
Get access Rights & Permissions [Opens in a new window]

Abstract

We introduce the optimal stopping problem of an infinite sequence of records associated with a planar Poisson process. This problem serves as a limiting form of the classical full information best-choice problem. A link between the finite problem and its limiting form is established via embedding n i.i.d. observations into the planar process.

Keywords

BEST-CHOICE PROBLEMPOISSON PROCESSRECORDS

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 60G70: Extreme value theory; extremal processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 3 , September 1996 , pp. 678 - 687
Copyright
Copyright © Applied Probability Trust 1996 

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

Berezovskiy, B. A. and Gnedin, A. V. (1984) The Best Choice Problem. Nauka, Moscow.Google Scholar
Bruss, E. T. and Rogers, L. C. G. (1991) Embedding optimal selection problems in a Poisson process. Stock Proc. Appl. 38, 267–278.Google Scholar
Gilbert, J. and Mosteller, F. (1966) Recognizing the maximum of a sequence. J. Amer. Statist. Assoc. 61, 35–73.Google Scholar
Gnedin, A. V. and Sakaguchi, M. (1992) On a best choice problem related to the Poisson process. In Proc. Joint Summer Research Conf. on Strategies for Sequential Search and Selection in Real Time, Amherst, MA, June 21-27, 1990. ed. Bruss, F. T., Ferguson, T. S. and Samuels, S. M. American Mathematical Society, Providence, RI.Google Scholar
Pfeifer, D. (1989) Extremal processes, secretary problems and the Me law. J. Appl. Prob. 27, 722–733.Google Scholar
Pickands, J. (1971) The two-dimensional Poisson process and extremal processes. J. Appl. Prob. 8, 745–756.Google Scholar
Resnick, S. I. (1987) Extreme Values, Regular Variation and Point Processes. Springer, New York.CrossRefGoogle Scholar
Sakaguchi, M. (1976) Optimal stopping problems for randomly arriving offers. Math. Japonica 21, 201–217.Google Scholar
Samuels, S. M. (1982) Exact solutions for the full information best choice problem. Purdue Univ. Stat. Dept. Mimeo Series 82–17.Google Scholar
Samuels, S. M. (1991) Secretary problems. In Handbook of Sequential Analysis , ed. Ghosh, B. K. and Sen, P. K. Marcel Dekker, Boston. pp. 381–405.Google Scholar