Edgeworth type expansion of ruin probability under Lévy risk processes in the small loading asymptotics

Yasutaka Shimizu

doi:10.1080/03461238.2012.755937

Edgeworth type expansion of ruin probability under Lévy risk processes in the small loading asymptotics

Yasutaka Shimizu^*

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

This paper presents an asymptotic expansion of the ultimate ruin probability under Lévy insurance risks as the loading factor tends to zero. The expansion formula is obtained via the Edgeworth type expansion for compound geometric distributions. We give higher-order expansion of the ruin probability, any order of which is available in explicit form, and discuss a certain type of validity of the expansion. We shall also give applications to evaluation of the VaR-type risk measure due to ruin, and the scale function of spectrally negative Lévy processes.

Original language	English
Pages (from-to)	620-648
Number of pages	29
Journal	Scandinavian Actuarial Journal
Issue number	7
DOIs	https://doi.org/10.1080/03461238.2012.755937
Publication status	Published - 2014 Oct
Externally published	Yes

Keywords

Edgeworth type expansion
Lévy insurance risk
compound geometric sum
ruin probability
small safety loading

ASJC Scopus subject areas

Statistics and Probability
Economics and Econometrics
Statistics, Probability and Uncertainty

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10.1080/03461238.2012.755937

Cite this

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title = "Edgeworth type expansion of ruin probability under L{\'e}vy risk processes in the small loading asymptotics",

abstract = "This paper presents an asymptotic expansion of the ultimate ruin probability under L{\'e}vy insurance risks as the loading factor tends to zero. The expansion formula is obtained via the Edgeworth type expansion for compound geometric distributions. We give higher-order expansion of the ruin probability, any order of which is available in explicit form, and discuss a certain type of validity of the expansion. We shall also give applications to evaluation of the VaR-type risk measure due to ruin, and the scale function of spectrally negative L{\'e}vy processes.",

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note = "Funding Information: This work was done during the visit of the first author to Concordia University in 2011. He is grateful to this university for its support. This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Young Scientists (B), 2011, no. 21740073, and Japan Science and Technology Agency, CREST.",

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N2 - This paper presents an asymptotic expansion of the ultimate ruin probability under Lévy insurance risks as the loading factor tends to zero. The expansion formula is obtained via the Edgeworth type expansion for compound geometric distributions. We give higher-order expansion of the ruin probability, any order of which is available in explicit form, and discuss a certain type of validity of the expansion. We shall also give applications to evaluation of the VaR-type risk measure due to ruin, and the scale function of spectrally negative Lévy processes.

AB - This paper presents an asymptotic expansion of the ultimate ruin probability under Lévy insurance risks as the loading factor tends to zero. The expansion formula is obtained via the Edgeworth type expansion for compound geometric distributions. We give higher-order expansion of the ruin probability, any order of which is available in explicit form, and discuss a certain type of validity of the expansion. We shall also give applications to evaluation of the VaR-type risk measure due to ruin, and the scale function of spectrally negative Lévy processes.

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KW - Lévy insurance risk

KW - compound geometric sum

KW - ruin probability

KW - small safety loading

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Edgeworth type expansion of ruin probability under Lévy risk processes in the small loading asymptotics

Abstract

Keywords

ASJC Scopus subject areas

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