### Abstract

Given a renewal process {S _{n}} _{n≥1} and a fixed terminal time T > 0, we want to find a strategy that maximizes the probability of stopping, without recall, at the last renewal up to T. We give a simple criterion to guarantee that the optimal strategy is of threshold type. This simple criterion is applied to several cases, including a problem of optimal stopping on patterns discussed in Bruss and Louchard (2003).

Original language | English |
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Pages (from-to) | 725-733 |

Number of pages | 9 |

Journal | Statistica Sinica |

Volume | 17 |

Issue number | 2 |

Publication status | Published - 2007 Apr 1 |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Hsiau, S. R. (2007). Stopping at the last renewal up to a terminal time.

*Statistica Sinica*,*17*(2), 725-733.