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- Title
ON THE OPTIMAL STOPPING PROBLEMS WITH MONOTONE THRESHOLDS.
- Authors
MITSUSHI TAMAKI
- 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.
- Subjects
MONOTONE operators; OPTIMAL control theory; PROBLEM solving; SECRETARY problem (Probability theory); POISSON processes
- Publication
Journal of Applied Probability, 2015, Vol 52, Issue 4, p926
- ISSN
0021-9002
- Publication type
Article
- DOI
10.1239/jap/1450802744