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Statistical Analysis of Natural Events in the United States

Author

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  • Charles Levi,
  • Partrat, Christian

Abstract

A statistical analysis is performed on natural events which can produce important damages to insurers. The analysis is based on hurricanes which have been observed in the United States between 1954 et 1986. At first, independence between the number and the amount of the losses is examined. Different distributions (Poisson and negative binomial for frequency and exponential, Pareto and lognormal for severity) are tested. Along classical tests as chi-square, Kolmogorov-Smirnov and non parametric tests, a test with weights on the upper tail of the distribution is used: the Anderson – Darling test. Confidence intervals for the probability of occurrence of a claim and expected frequency for different potential levels of claims are derived. The Poisson Log-normal model gives a very good fit to the data.

Suggested Citation

  • Charles Levi, & Partrat, Christian, 1991. "Statistical Analysis of Natural Events in the United States," ASTIN Bulletin, Cambridge University Press, vol. 21(2), pages 253-276, November.
    • Handle: RePEc:cup:astinb:v:21:y:1991:i:02:p:253-276_00
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    Cited by:

    1. Burnecki, Krzysztof & Giuricich, Mario Nicoló & Palmowski, Zbigniew, 2019. "Valuation of contingent convertible catastrophe bonds — The case for equity conversion," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 238-254.
    2. Ma, Zong-Gang & Ma, Chao-Qun, 2013. "Pricing catastrophe risk bonds: A mixed approximation method," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 243-254.
    3. Braun, Alexander, 2011. "Pricing catastrophe swaps: A contingent claims approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 520-536.
    4. Tim Keighley & Thomas Longden & Supriya Mathew & Stefan Trück, 2014. "Quantifying Catastrophic and Climate Impacted Hazards Based on Local Expert Opinions," Working Papers 2014.93, Fondazione Eni Enrico Mattei.
    5. Chang, Carolyn W. & Chang, Jack S.K. & Lu, WeLi, 2010. "Pricing catastrophe options with stochastic claim arrival intensity in claim time," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 24-32, January.
    6. Chang, Carolyn W. & Chang, Jack S.K. & Lu, WeiLi, 2008. "Pricing catastrophe options in discrete operational time," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 422-430, December.
    7. Wang, Xingchun, 2016. "Catastrophe equity put options with target variance," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 79-86.
    8. Min Deng & Mostafa Aminzadeh & Min Ji, 2021. "Bayesian Predictive Analysis of Natural Disaster Losses," Risks, MDPI, vol. 9(1), pages 1-23, January.
    9. Wang, Xingchun, 2020. "Catastrophe equity put options with floating strike prices," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    10. Wang, Xingchun, 2019. "Valuation of new-designed contracts for catastrophe risk management," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).

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