## 抄録

In this paper we deal with an optimal stopping problem whose objective is to maximize the probability of selecting k out of the last l successes, given a sequence of independent Bernoulli trials of length N, where k and l are predetermined integers satisfying 1≤k≤l<N. This problem includes some odds problems as special cases, e.g. Bruss' odds problem, Bruss and Paindaveine's problem of selecting the last l successes, and Tamaki's multiplicative odds problem for stopping at any of the last m successes. We show that an optimal stopping rule is obtained by a threshold strategy. We also present the tight lower bound and an asymptotic lower bound for the probability of a win. Interestingly, our asymptotic lower bound is attained by using a variation of the well-known secretary problem, which is a special case of the odds problem. Our approach is based on the application of Newton's inequalities and optimization technique, which gives a unified view to the previous works.

本文言語 | English |
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ページ（範囲） | 12-22 |

ページ数 | 11 |

ジャーナル | Journal of Applied Probability |

巻 | 54 |

号 | 1 |

DOI | |

出版ステータス | Published - 2017 3月 1 |

## ASJC Scopus subject areas

- 統計学および確率
- 数学 (全般)
- 統計学、確率および不確実性