Abstract
A statistical inference for ruin probability from a certain discrete sample of the surplus is discussed under a spectrally negative Lévy insurance risk. We consider the Laguerre series expansion of ruin probability, and provide an estimator for any of its partial sums by computing the coefficients of the expansion. We show that the proposed estimator is asymptotically normal and consistent with the optimal rate of convergence and estimable asymptotic variance. This estimator enables not only a point estimation of ruin probability but also an approximated interval estimation and testing hypothesis.
| Original language | English |
|---|---|
| Article number | 37 |
| Journal | Risks |
| Volume | 7 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2019 Jun 1 |
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Keywords
- Asymptotic normality
- Discrete observations
- Laguerre polynomial
- Ruin probability
- Spectrally negative Lévy process
ASJC Scopus subject areas
- Accounting
- Economics, Econometrics and Finance (miscellaneous)
- Strategy and Management
Cite this
Asymptotically normal estimators of the ruin probability for lévy insurance surplus from discrete samples. / Shimizu, Yasutaka; Zhang, Zhimin.
In: Risks, Vol. 7, No. 2, 37, 01.06.2019.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Asymptotically normal estimators of the ruin probability for lévy insurance surplus from discrete samples
AU - Shimizu, Yasutaka
AU - Zhang, Zhimin
PY - 2019/6/1
Y1 - 2019/6/1
N2 - A statistical inference for ruin probability from a certain discrete sample of the surplus is discussed under a spectrally negative Lévy insurance risk. We consider the Laguerre series expansion of ruin probability, and provide an estimator for any of its partial sums by computing the coefficients of the expansion. We show that the proposed estimator is asymptotically normal and consistent with the optimal rate of convergence and estimable asymptotic variance. This estimator enables not only a point estimation of ruin probability but also an approximated interval estimation and testing hypothesis.
AB - A statistical inference for ruin probability from a certain discrete sample of the surplus is discussed under a spectrally negative Lévy insurance risk. We consider the Laguerre series expansion of ruin probability, and provide an estimator for any of its partial sums by computing the coefficients of the expansion. We show that the proposed estimator is asymptotically normal and consistent with the optimal rate of convergence and estimable asymptotic variance. This estimator enables not only a point estimation of ruin probability but also an approximated interval estimation and testing hypothesis.
KW - Asymptotic normality
KW - Discrete observations
KW - Laguerre polynomial
KW - Ruin probability
KW - Spectrally negative Lévy process
UR - http://www.scopus.com/inward/record.url?scp=85066961415&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85066961415&partnerID=8YFLogxK
U2 - 10.3390/risks7020037
DO - 10.3390/risks7020037
M3 - Article
AN - SCOPUS:85066961415
VL - 7
JO - Risks
JF - Risks
SN - 2227-9091
IS - 2
M1 - 37
ER -