Estimation of ruin probabilities by means of hazard rates

Claudia Klüppelberg

doi:10.1016/0167-6687(89)90003-6

Estimation of ruin probabilities by means of hazard rates

Claudia Klüppelberg

University of Mannheim

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

We show that the asymptotic behaviour of the hazard rate of the claim-size distribution determines not only the singular point of the moment generating function but can also be used to estimate the asymptotic ruin probability. We shall use these results to classify the relevant claim-size distributions and calculate the respective ruin probabilities. Hereby we shall concentrate on the case where Cramér's method does not work.

Original language	English
Pages (from-to)	279-285
Number of pages	7
Journal	Insurance: Mathematics and Economics
Volume	8
Issue number	4
DOIs	https://doi.org/10.1016/0167-6687(89)90003-6
State	Published - Dec 1989
Externally published	Yes

Keywords

Asymptotic ruin probability
Convolution-equivalent distributions
Non-Cramér case
Subexponential distributions

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10.1016/0167-6687(89)90003-6

Cite this

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title = "Estimation of ruin probabilities by means of hazard rates",

abstract = "We show that the asymptotic behaviour of the hazard rate of the claim-size distribution determines not only the singular point of the moment generating function but can also be used to estimate the asymptotic ruin probability. We shall use these results to classify the relevant claim-size distributions and calculate the respective ruin probabilities. Hereby we shall concentrate on the case where Cram{\'e}r's method does not work.",

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AB - We show that the asymptotic behaviour of the hazard rate of the claim-size distribution determines not only the singular point of the moment generating function but can also be used to estimate the asymptotic ruin probability. We shall use these results to classify the relevant claim-size distributions and calculate the respective ruin probabilities. Hereby we shall concentrate on the case where Cramér's method does not work.

KW - Asymptotic ruin probability

KW - Convolution-equivalent distributions

KW - Non-Cramér case

KW - Subexponential distributions

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DO - 10.1016/0167-6687(89)90003-6

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VL - 8

SP - 279

EP - 285

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

IS - 4

ER -

Estimation of ruin probabilities by means of hazard rates

Abstract

Keywords

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