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Bayesian approaches for analyzing earthquake catastrophic risk

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  • Li, Yunxian
  • Tang, Niansheng
  • Jiang, Xuejun

Abstract

Extreme value theory has been widely used in analyzing catastrophic risk. The theory mentioned that the generalized Pareto distribution (GPD) could be used to estimate the limiting distribution of the excess value over a certain threshold; thus the tail behaviors are analyzed. However, the central behavior is important because it may affect the estimation of model parameters in GPD, and the evaluation of catastrophic insurance premiums also depends on the central behavior. This paper proposes four mixture models to model earthquake catastrophic loss and proposes Bayesian approaches to estimate the unknown parameters and the threshold in these mixture models. MCMC methods are used to calculate the Bayesian estimates of model parameters, and deviance information criterion values are obtained for model comparison. The earthquake loss of Yunnan province is analyzed to illustrate the proposed methods. Results show that the estimation of the threshold and the shape and scale of GPD are quite different. Value-at-risk and expected shortfall for the proposed mixture models are calculated under different confidence levels.

Suggested Citation

  • Li, Yunxian & Tang, Niansheng & Jiang, Xuejun, 2016. "Bayesian approaches for analyzing earthquake catastrophic risk," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 110-119.
    • Handle: RePEc:eee:insuma:v:68:y:2016:i:c:p:110-119
    DOI: 10.1016/j.insmatheco.2016.02.004
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    References listed on IDEAS

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    Cited by:

    1. Laudagé, Christian & Desmettre, Sascha & Wenzel, Jörg, 2019. "Severity modeling of extreme insurance claims for tariffication," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 77-92.
    2. Xuejun Jiang & Yunxian Li & Aijun Yang & Ruowei Zhou, 2020. "Bayesian semiparametric quantile regression modeling for estimating earthquake fatality risk," Empirical Economics, Springer, vol. 58(5), pages 2085-2103, May.
    3. Gu, Zheng & Li, Yunxian & Zhang, Minghui & Liu, Yifei, 2023. "Modelling economic losses from earthquakes using regression forests: Application to parametric insurance," Economic Modelling, Elsevier, vol. 125(C).
    4. Pai, Jeffrey & Li, Yunxian & Yang, Aijun & Li, Chenxu, 2022. "Earthquake parametric insurance with Bayesian spatial quantile regression," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 1-12.

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