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On the optimal stopping problems with monotone thresholds

Part of: Stochastic processes Sequential methods

Published online by Cambridge University Press:  30 March 2016

Mitsushi Tamaki
Mitsushi Tamaki*
Affiliation:
Aichi University
*
∗Postal address: Department of Business Administration, Aichi University, Nagoya Campus, Hiraike 4–60–6, Nakamura, Nagoya, Aichi, 453-8777, Japan. Email address: [email protected]
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Abstract

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As a class of optimal stopping problems with monotone thresholds, we define the candidate-choice problem (CCP) and derive two formulae for calculating its expected payoff. We apply the first formula to a particular CCP, i.e. the best-choice duration problem treated by Ferguson et al. (1992). The recall case is also examined as a comparison. We also derive the distribution of the stopping time of the CCP and find, as a by-product, that the best-choice problem has a remarkable feature in that the optimal probability of choosing the best is just the expected value of the (proportional) stopping time. The similarity between the best-choice duration problem and the best-choice problem with uniform freeze studied by Samuel-Cahn (1996) is recognized.

Keywords

Secretary problembest-choice problemduration problembest-choice duration problemcandidate-choice problemmonotone ruleplanar Poisson process

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 62L15: Optimal stopping
Type
Research Papers
Information
Journal of Applied Probability , Volume 52 , Issue 4 , December 2015 , pp. 926 - 940
Copyright
Copyright © Applied Probability Trust 2015 

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