Journal of Applied Probability
- J. Appl. Probab.
- Volume 51, Number 3 (2014), 885-889.
A note on a lower bound for the multiplicative odds theorem of optimal stopping
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.
J. Appl. Probab., Volume 51, Number 3 (2014), 885-889.
First available in Project Euclid: 5 September 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
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