Maximizing the expected duration of owning a relatively best object in a
Poisson process with rankable observations
Aiko Kurushima and Katsunori Ano
Source: J. Appl. Probab.
Volume 46, Number 2
(2009), 402-414.
Abstract
Suppose that an unknown number of objects arrive sequentially
according to a Poisson process with random intensity λ on
some fixed time interval [0,T]. We assume a gamma prior density
Gλ(r, 1/a) for λ. Furthermore, we suppose that
all arriving objects can be ranked uniquely among all preceding
arrivals. Exactly one object can be selected. Our aim is to find a
stopping time (selection time) which maximizes the time during
which the selected object will stay relatively best. Our main
result is the following. It is optimal to select the ith object
that is relatively best and arrives at some time si(r)
onwards. The value of si(r)
can be obtained for each r and i as the unique root of a
deterministic equation.
Primary Subjects: 60G40
Secondary Subjects: 62L15
Keywords: Optimal stopping problem; secretary problem; Poisson arrival; duration problem
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1245676096
Digital Object Identifier: doi:10.1239/jap/1245676096
Zentralblatt MATH identifier:
05578815
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