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

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

1 Citation (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

Access to Document

10.1080/03461238.2012.755937

Fingerprint Dive into the research topics of 'Edgeworth type expansion of ruin probability under Lévy risk processes in the small loading asymptotics'. Together they form a unique fingerprint.

Cite this

@article{fe10ed0cb09545578b0f294c60bb583c,

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.",

keywords = "Edgeworth type expansion, L{\'e}vy insurance risk, compound geometric sum, ruin probability, small safety loading",

author = "Yasutaka Shimizu",

year = "2014",

month = oct,

doi = "10.1080/03461238.2012.755937",

language = "English",

pages = "620--648",

journal = "Scandinavian Actuarial Journal",

issn = "0346-1238",

publisher = "Taylor and Francis Ltd.",

number = "7",

}

TY - JOUR

T1 - Edgeworth type expansion of ruin probability under Lévy risk processes in the small loading asymptotics

AU - Shimizu, Yasutaka

PY - 2014/10

Y1 - 2014/10

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.

KW - Edgeworth type expansion

KW - Lévy insurance risk

KW - compound geometric sum

KW - ruin probability

KW - small safety loading

UR - http://www.scopus.com/inward/record.url?scp=84904399389&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904399389&partnerID=8YFLogxK

U2 - 10.1080/03461238.2012.755937

DO - 10.1080/03461238.2012.755937

M3 - Article

AN - SCOPUS:84904399389

SP - 620

EP - 648

JO - Scandinavian Actuarial Journal

JF - Scandinavian Actuarial Journal

SN - 0346-1238

IS - 7

ER -