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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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

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

First available in Project Euclid: 5 September 2014

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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