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 | |
| Publication status | Published - 2014 |
| Externally published | Yes |
Fingerprint
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
Edgeworth type expansion of ruin probability under Lévy risk processes in the small loading asymptotics. / Shimizu, Yasutaka.
In: Scandinavian Actuarial Journal, No. 7, 2014, p. 620-648.Research output: Contribution to journal › Article
}
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 -