### Abstract

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.

Original language | English |
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Pages (from-to) | 125-149 |

Number of pages | 25 |

Journal | Mathematical Methods of Statistics |

Volume | 20 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2011 Jun |

Externally published | Yes |

### Fingerprint

### Keywords

- discrete observations
- expected discounted penalty function
- ISE-consistency
- Lévy risk process
- regularized Laplace inversion

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Statistics and Probability

### Cite this

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

Research output: Contribution to journal › Article

*Mathematical Methods of Statistics*, vol. 20, no. 2, pp. 125-149. https://doi.org/10.3103/S1066530711020037

}

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 -