TY - JOUR
T1 - Parametric inference for ruin probability in the classical risk model
AU - Oshime, Takayoshi
AU - Shimizu, Yasutaka
N1 - Funding Information:
The authors would like to thank two referees for their valuable suggestions which significantly improved the paper. The second author is supported by JSPS KAKENHI Grant-in-Aid for Scientific Research (C), Grant Number JP15K05009 , and also by JST CREST .
Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2018/2
Y1 - 2018/2
N2 - Consider the classical insurance surplus model with a parametric family for the claim distribution. Although we can construct an asymptotically normal estimator of the ruin probability from the claim data, the asymptotic variance is not easy to estimate since it includes the derivative of the ruin probability with respect to the parameter. This paper gives an explicit asymptotic formula for the asymptotic variance, which is easy to estimate, and gives an asymptotic confidence interval of ruin probability.
AB - Consider the classical insurance surplus model with a parametric family for the claim distribution. Although we can construct an asymptotically normal estimator of the ruin probability from the claim data, the asymptotic variance is not easy to estimate since it includes the derivative of the ruin probability with respect to the parameter. This paper gives an explicit asymptotic formula for the asymptotic variance, which is easy to estimate, and gives an asymptotic confidence interval of ruin probability.
KW - Asymptotic confidence interval
KW - Cramér approximation
KW - Delta method
KW - Ruin probability
KW - Small claims
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U2 - 10.1016/j.spl.2017.09.020
DO - 10.1016/j.spl.2017.09.020
M3 - Article
AN - SCOPUS:85033447781
SN - 0167-7152
VL - 133
SP - 28
EP - 37
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
ER -