TY - JOUR
T1 - Asymptotically normal estimators of the ruin probability for lévy insurance surplus from discrete samples
AU - Shimizu, Yasutaka
AU - Zhang, Zhimin
N1 - Funding Information:
Funding: The first author is supported by JSPS KAKENHI Grant-in-Aid for Scientific Research (A), Grant Number 17H01100. The second author is supported by the National Natural Science Foundation of China (11871121, 11471058), MOE (Ministry of Education in China) Project of Humanities and Social Sciences (16YJC910005) and Fundamental Research Funds for the Central Universities (2018CDQYST0016).
Publisher Copyright:
© 2019 by the author. Licensee MDPI, Basel, Switzerland.
PY - 2019/6
Y1 - 2019/6
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
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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 -