Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-24T09:16:18.344Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal stopping in a continuous search model

Published online by Cambridge University Press:  14 July 2016

Dror Zuckerman
Dror Zuckerman*
Affiliation:
The Hebrew University of Jerusalem
*
∗Present address: Management Science Division, The University of British Columbia, 2053 Main Mall, Vancouver, B.C., Canada V6T 1Y8.
Get access Rights & Permissions [Opens in a new window]

Abstract

We examine a continuous search model in which rewards (e.g. job offers in a search model in the labor market, price offers for a given asset, etc.) are received randomly according to a renewal process determined by a known distribution function. The rewards are non-negative independent and have a common distribution with finite mean. Over the search period there is a constant cost per unit time. The searcher's objective is to choose a stopping time at which he receives the highest available reward (offer), so as to maximize the net expected discounted return. If the interarrival time distribution in the renewal process is new better than used (NBU), it is shown that the optimal stopping strategy possesses the control limit property. The term ‘control limit policy' refers to a strategy in which we accept the first reward (offer) which exceeds a critical control level ξ.

Keywords

RENEWAL PROCESSCONTROL LIMIT POLICYSTRONG MARKOV PROCESSLAPLACE TRANSFORMNEW BETTER THAN USEDNEW BETTER THAN USED IN EXPECTATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 23 , Issue 2 , June 1986 , pp. 514 - 518
Copyright
Copyright © Applied Probability Trust 1986 

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

[1] Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.Google Scholar
[2] Lippman, S. A. and Mccall, J. J. (1976) The economics of job search: a survey. Econ. Inquiry 14, 155–189.Google Scholar
[3] Stigler, G. J. (1961) The economics of information. J. Political Econ. 69, 213–225.Google Scholar
[4] Stigler, G. J. (1962) Information in the labor market. J. Political Econ. 70, 94–104.CrossRefGoogle Scholar
[5] Taylor, H. M. (1968) Optimal stopping in a Markov process. Ann. Math. Statist. 39, 1333–1344.Google Scholar
[6] Telser, L. (1973) Searching for the lowest price. Amer. Econom. Rev. 63, 40–49.Google Scholar
[7] Zuckerman, D. (1985) On preserving the reservation wage property in a continuous job search model. J. Econ. Theory 34, 175–179.Google Scholar