### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 28-37 |

Number of pages | 10 |

Journal | Statistics and Probability Letters |

Volume | 133 |

DOIs | |

Publication status | Published - 2018 Feb 1 |

### Fingerprint

### Keywords

- Asymptotic confidence interval
- Cramér approximation
- Delta method
- Ruin probability
- Small claims

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

**Parametric inference for ruin probability in the classical risk model.** / Oshime, Takayoshi; Shimizu, Yasutaka.

Research output: Contribution to journal › Article

*Statistics and Probability Letters*, vol. 133, pp. 28-37. https://doi.org/10.1016/j.spl.2017.09.020

}

TY - JOUR

T1 - Parametric inference for ruin probability in the classical risk model

AU - Oshime, Takayoshi

AU - Shimizu, Yasutaka

PY - 2018/2/1

Y1 - 2018/2/1

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

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

U2 - 10.1016/j.spl.2017.09.020

DO - 10.1016/j.spl.2017.09.020

M3 - Article

VL - 133

SP - 28

EP - 37

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

ER -