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 .

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

UR - http://www.scopus.com/inward/record.url?scp=85033447781&partnerID=8YFLogxK

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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

VL - 133

SP - 28

EP - 37

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

ER -