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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.
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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 

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