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Modeling Catastrophes and their Impact on Insurance Portfolios

Author

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  • Hélène Cossette
  • Thierry Duchesne
  • Étienne Marceau

Abstract

The authors propose a general individual catastrophe risk model that allows damage ratios to be random functions of the catastrophe intensity. They derive some distributional properties of the insured risks and of the aggregate catastrophic loss under this model. Through the model and ruin probability calculations, they formally illustrate the well-known fact that the catastrophe risk cannot be diversified through premium collection alone, as is the case with the usual “day-to-day” risk, even for an arbitrary large portfolio. They also derive some risk orderings between different catastrophe portfolios and show that the risk level of a realistic portfolio falls between that of a portfolio of comonotonic risks and that of a portfolio of independent risks. Finally, the authors illustrate their findings with a numerical example inspired from earthquake insurance.

Suggested Citation

  • Hélène Cossette & Thierry Duchesne & Étienne Marceau, 2003. "Modeling Catastrophes and their Impact on Insurance Portfolios," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 1-22.
    • Handle: RePEc:taf:uaajxx:v:7:y:2003:i:4:p:1-22
    DOI: 10.1080/10920277.2003.10596114
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    Cited by:

    1. Victor Cardenas, 2024. "Financial climate risk: a review of recent advances and key challenges," Papers 2404.07331, arXiv.org.
    2. Fabio Pizzutilo & Elisabetta Venezia, 2018. "Are catastrophe bonds effective financial instruments in the transport and infrastructure industries? Evidence from international financial markets," Business and Economic Horizons (BEH), Prague Development Center, vol. 14(2), pages 256-267, April.
    3. Mercè Claramunt, M. & Lefèvre, Claude & Loisel, Stéphane & Montesinos, Pierre, 2022. "Basis risk management and randomly scaled uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 123-139.
    4. Brodin, Erik & Rootzén, Holger, 2009. "Univariate and bivariate GPD methods for predicting extreme wind storm losses," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 345-356, June.
    5. Claude Lefèvre & Stéphane Loisel & Pierre Montesinos, 2020. "Bounding basis risk using s-convex orders on Beta-unimodal distributions," Working Papers hal-02611208, HAL.
    6. Kellenberg, Derek K. & Mobarak, Ahmed Mushfiq, 2008. "Does rising income increase or decrease damage risk from natural disasters?," Journal of Urban Economics, Elsevier, vol. 63(3), pages 788-802, May.
    7. Rafał Wójcik & Charlie Wusuo Liu, 2022. "Bivariate Copula Trees for Gross Loss Aggregation with Positively Dependent Risks," Risks, MDPI, vol. 10(8), pages 1-24, July.
    8. Patricia Born & Randy Dumm & Mark E. Johnson, 2023. "Epistemic uncertainty in catastrophe models—A base level examination," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 26(2), pages 247-269, July.

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