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Interval estimation of the ruin probability in the classical compound Poisson risk model

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  • You, Honglong
  • Guo, Junyi
  • Jiang, Jiancheng

Abstract

Estimating ruin probability is an important problem in insurance. Zhang et al. (2014) proposed a novel nonparametric estimation method for the ruin probability in the classical risk model with unknown claim size distribution, based on the Fourier transform and the kernel density estimation. However, asymptotic distributions of their estimators are unknown, which hampers statistical inference for the ruin probability. The authors establish asymptotic normal distributions of the estimators with known and with unknown intensity. Since the standard deviations of estimators are hard to estimate, a bootstrap method is advanced to estimate them. This allows one to construct a confidence interval estimate of the ruin probability. Furthermore, a new method is proposed to fast calculate the estimates, and the numerical results are stable and free of the “curse of large initial surplus” problem. Simulations are conducted to demonstrate nice finite sample performance of the estimators. A real dataset from a car insurance company is analyzed for illustrating the use of the proposed methodology.

Suggested Citation

  • You, Honglong & Guo, Junyi & Jiang, Jiancheng, 2020. "Interval estimation of the ruin probability in the classical compound Poisson risk model," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:csdana:v:144:y:2020:i:c:s0167947319302452
    DOI: 10.1016/j.csda.2019.106890
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    References listed on IDEAS

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    Cited by:

    1. Chongkai Xie & Honglong You, 2024. "A Threshold Estimator for Ruin Probability Using the Fourier-Cosine Method in the Wiener–Poisson Risk Model," Mathematics, MDPI, vol. 12(18), pages 1-14, September.
    2. Xie, Jiayi & Zhang, Zhimin, 2020. "Statistical estimation for some dividend problems under the compound Poisson risk model," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 101-115.
    3. Yuan Gao & Honglong You, 2021. "The Speed of Convergence of the Threshold Estimator of Ruin Probability under the Tempered α -Stable Lévy Subordinator," Mathematics, MDPI, vol. 9(21), pages 1-9, October.
    4. Yuan Gao & Lingju Chen & Jiancheng Jiang & Honglong You, 2020. "Nonparametric Estimation of the Ruin Probability in the Classical Compound Poisson Risk Model," JRFM, MDPI, vol. 13(12), pages 1-12, November.
    5. Kang Hu & Ya Huang & Yingchun Deng, 2023. "Estimating the Gerber–Shiu Function in the Two-Sided Jumps Risk Model by Laguerre Series Expansion," Mathematics, MDPI, vol. 11(9), pages 1-30, April.
    6. Wen Su & Yunyun Wang, 2021. "Estimating the Gerber-Shiu Function in Lévy Insurance Risk Model by Fourier-Cosine Series Expansion," Mathematics, MDPI, vol. 9(12), pages 1-18, June.

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