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

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)620-648
Number of pages29
JournalScandinavian Actuarial Journal
Issue number7
DOIs
Publication statusPublished - 2014
Externally publishedYes

Fingerprint

Probability of Ruin
Risk Process
Ruin Probability
Compound Distribution
Scale Function
Geometric distribution
Risk Measures
Insurance
Asymptotic Expansion
Tend
Higher Order
Probability of ruin
Risk process
Evaluation
Zero
Ruin probability

Keywords

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

ASJC Scopus subject areas

  • Economics and Econometrics
  • Statistics, Probability and Uncertainty
  • Statistics and Probability

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 = "compound geometric sum, Edgeworth type expansion, L{\'e}vy insurance risk, ruin probability, small safety loading",
author = "Yasutaka Shimizu",
year = "2014",
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

Y1 - 2014

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 - compound geometric sum

KW - Edgeworth type expansion

KW - Lévy insurance risk

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 -