Parametric inference for ruin probability in the classical risk model

Takayoshi Oshime, Yasutaka Shimizu

Research output: Contribution to journalArticle

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 28-37 10 Statistics and Probability Letters 133 https://doi.org/10.1016/j.spl.2017.09.020 Published - 2018 Feb 1

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Parametric Inference
Ruin Probability
Asymptotic Variance
Probability of Ruin
Asymptotic Formula
Insurance
Estimate
Confidence interval
Explicit Formula
Estimator
Derivative
Model
Ruin probability
Asymptotic variance
Classical risk model
Inference
Family
Probability of ruin
Derivatives
Surplus

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

In: Statistics and Probability Letters, Vol. 133, 01.02.2018, p. 28-37.

Research output: Contribution to journalArticle

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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.",
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