### Abstract

We study the asymptotics for the maximum on a random time interval of a random walk with a long-tailed distribution of its increments and negative drift. We extend to a general stopping time a result by Asmussen, simplify its proof and give some converses.

Original language | English |
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Pages (from-to) | 37-53 |

Number of pages | 17 |

Journal | Annals of Applied Probability |

Volume | 13 |

Issue number | 1 |

Publication status | Published - Feb 2003 |

### Keywords

- Long-tailed distribution
- Ruin probability
- Subexponential distribution

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## Cite this

Foss, S., & Zachary, S. (2003). The maximum on a random time interval of a random walk with long-tailed increments and negative drift.

*Annals of Applied Probability*,*13*(1), 37-53.