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December 2015 On the optimal stopping problems with monotone thresholds
Mitsushi Tamaki
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J. Appl. Probab. 52(4): 926-940 (December 2015). DOI: 10.1239/jap/1450802744

Abstract

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.

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Mitsushi Tamaki. "On the optimal stopping problems with monotone thresholds." J. Appl. Probab. 52 (4) 926 - 940, December 2015. https://doi.org/10.1239/jap/1450802744

Information

Published: December 2015
First available in Project Euclid: 22 December 2015

zbMATH: 1336.60080
MathSciNet: MR3439163
Digital Object Identifier: 10.1239/jap/1450802744

Subjects:
Primary: 60G40
Secondary: 62L15

Rights: Copyright © 2015 Applied Probability Trust

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Vol.52 • No. 4 • December 2015
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