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Optimal stopping in a continuous search model. (English) Zbl 0592.60081
Summary: 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 posesses 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 \(\xi\).

MSC:
60K10 Applications of renewal theory (reliability, demand theory, etc.)
60G40 Stopping times; optimal stopping problems; gambling theory
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
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