Journal of Applied Probability

A note on a lower bound for the multiplicative odds theorem of optimal stopping

Tomomi Matsui and Katsunori Ano

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Abstract

In this note we present a bound of the optimal maximum probability for the multiplicative odds theorem of optimal stopping theory. We deal with an optimal stopping problem that maximizes the probability of stopping on any of the last m successes of a sequence of independent Bernoulli trials of length N, where m and N are predetermined integers satisfying 1 ≤ m < N. This problem is an extension of Bruss' (2000) odds problem. In a previous work, Tamaki (2010) derived an optimal stopping rule. We present a lower bound of the optimal probability. Interestingly, our lower bound is attained using a variation of the well-known secretary problem, which is a special case of the odds problem.

Article information

Source
J. Appl. Probab., Volume 51, Number 3 (2014), 885-889.

Dates
First available in Project Euclid: 5 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1409932681

Digital Object Identifier
doi:10.1239/jap/1409932681

Mathematical Reviews number (MathSciNet)
MR3256234

Zentralblatt MATH identifier
1312.60047

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Secondary: 60L15

Keywords
Optimal stopping odd problem lower bound secretary problem Maclaurin's inequality

Citation

Matsui, Tomomi; Ano, Katsunori. A note on a lower bound for the multiplicative odds theorem of optimal stopping. J. Appl. Probab. 51 (2014), no. 3, 885--889. doi:10.1239/jap/1409932681. https://projecteuclid.org/euclid.jap/1409932681


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