### 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 previouswork, 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..

Original language | English |
---|---|

Pages (from-to) | 885-889 |

Number of pages | 5 |

Journal | Journal of Applied Probability |

Volume | 51 |

Issue number | 3 |

Publication status | Published - 2014 Sep 1 |

### Fingerprint

### Keywords

- Lower bound
- Maclaurin's inequality
- Odd problem
- Optimal stopping
- Secretary problem

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Journal of Applied Probability*,

*51*(3), 885-889.

**A note on a lower bound for the multiplicative odds theorem of optimal stopping.** / Matsui, Tomomi; Ano, Katsunori.

Research output: Contribution to journal › Article

*Journal of Applied Probability*, vol. 51, no. 3, pp. 885-889.

}

TY - JOUR

T1 - A note on a lower bound for the multiplicative odds theorem of optimal stopping

AU - Matsui, Tomomi

AU - Ano, Katsunori

PY - 2014/9/1

Y1 - 2014/9/1

N2 - 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 previouswork, 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..

AB - 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 previouswork, 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..

KW - Lower bound

KW - Maclaurin's inequality

KW - Odd problem

KW - Optimal stopping

KW - Secretary problem

UR - http://www.scopus.com/inward/record.url?scp=84907729760&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907729760&partnerID=8YFLogxK

M3 - Article

VL - 51

SP - 885

EP - 889

JO - Journal of Applied Probability

JF - Journal of Applied Probability

SN - 0021-9002

IS - 3

ER -