### 抄録

We consider a generalized risk process which consists of a subordinator plus a spectrally negative Lévy process. Our interest is to estimate the expected discounted penalty function (EDPF) from a set of data which is practical in the insurance framework. We construct an empirical type estimator of the Laplace transform of the EDPF and obtain it by a regularized Laplace inversion. The asymptotic behavior of the estimator under a high frequency assumption is investigated.

元の言語 | English |
---|---|

ページ（範囲） | 125-149 |

ページ数 | 25 |

ジャーナル | Mathematical Methods of Statistics |

巻 | 20 |

発行部数 | 2 |

DOI | |

出版物ステータス | Published - 2011 6 |

外部発表 | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Statistics and Probability

### これを引用

**Estimation of the expected discounted penalty function for Lévy insurance risks.** / Shimizu, Yasutaka.

研究成果: Article

}

TY - JOUR

T1 - Estimation of the expected discounted penalty function for Lévy insurance risks

AU - Shimizu, Yasutaka

PY - 2011/6

Y1 - 2011/6

N2 - We consider a generalized risk process which consists of a subordinator plus a spectrally negative Lévy process. Our interest is to estimate the expected discounted penalty function (EDPF) from a set of data which is practical in the insurance framework. We construct an empirical type estimator of the Laplace transform of the EDPF and obtain it by a regularized Laplace inversion. The asymptotic behavior of the estimator under a high frequency assumption is investigated.

AB - We consider a generalized risk process which consists of a subordinator plus a spectrally negative Lévy process. Our interest is to estimate the expected discounted penalty function (EDPF) from a set of data which is practical in the insurance framework. We construct an empirical type estimator of the Laplace transform of the EDPF and obtain it by a regularized Laplace inversion. The asymptotic behavior of the estimator under a high frequency assumption is investigated.

KW - discrete observations

KW - expected discounted penalty function

KW - ISE-consistency

KW - Lévy risk process

KW - regularized Laplace inversion

UR - http://www.scopus.com/inward/record.url?scp=84859573976&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859573976&partnerID=8YFLogxK

U2 - 10.3103/S1066530711020037

DO - 10.3103/S1066530711020037

M3 - Article

AN - SCOPUS:84859573976

VL - 20

SP - 125

EP - 149

JO - Mathematical Methods of Statistics

JF - Mathematical Methods of Statistics

SN - 1066-5307

IS - 2

ER -