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Univariate and bivariate GPD methods for predicting extreme wind storm losses

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  • Brodin, Erik
  • Rootzén, Holger

Abstract

Wind storm and hurricane risks are attracting increased attention as a result of recent catastrophic events. The aim of this paper is to select, tailor, and develop extreme value methods for use in wind storm insurance. The methods are applied to the 1982-2005 losses for the largest Swedish insurance company, the Länsförsäkringar group. Both a univariate and a new bivariate Generalized Pareto Distribution (GPD) gave models which fitted the data well. The bivariate model led to lower estimates of risk, except for extreme cases, but taking statistical uncertainty into account the two models lead to qualitatively similar results. We believe that the bivariate model provided the most realistic picture of the real uncertainties. It additionally made it possible to explore the effects of changes in the insurance portfolio, and showed that loss distributions are rather insensitive to portfolio changes. We found a small trend in the sizes of small individual claims, but no other trends. Finally, we believe that companies should develop systematic ways of thinking about "not yet seen" disasters.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:44:y:2009:i:3:p:345-356
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    References listed on IDEAS

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    1. Dwight M. Jaffee & Thomas Russell, 1996. "Catastrophe Insurance, Capital Markets and Uninsurable Risks," Center for Financial Institutions Working Papers 96-12, Wharton School Center for Financial Institutions, University of Pennsylvania.
    2. 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.
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    Cited by:

    1. Zheng-wen Wang & Ling Tian, 2016. "How much catastrophe insurance fund needed in China for the ‘big one’? An estimation with comonotonicity method," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 84(1), pages 55-68, October.
    2. Alexandre Mornet & Thomas Opitz & Michel Luzi & Stéphane Loisel, 2015. "Index for predicting insurance claims from wind storms with an application in France," Post-Print hal-01081758, HAL.
    3. Buch-Kromann, Tine & Guillén, Montserrat & Linton, Oliver & Nielsen, Jens Perch, 2011. "Multivariate density estimation using dimension reducing information and tail flattening transformations," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 99-110, January.
    4. Maud Thomas & Holger Rootzén, 2022. "Real‐time prediction of severe influenza epidemics using extreme value statistics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(2), pages 376-394, March.
    5. Alexandre Mornet & Thomas Opitz & Michel Luzi & Stéphane Loisel, 2015. "Index for Predicting Insurance Claims from Wind Storms with an Application in France," Risk Analysis, John Wiley & Sons, vol. 35(11), pages 2029-2056, November.
    6. Rootzen, Holger & Segers, Johan & Wadsworth, Jenny, 2016. "Multivariate peaks over thresholds models," LIDAM Discussion Papers ISBA 2016018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Alexandre Mornet & Thomas Opitz & Michel Luzi & Stéphane Loisel, 2014. "Construction of an Index that links Wind Speeds and Strong Claim Rate of Insurers after a Storm in France," Working Papers hal-01081758, HAL.
    8. Kellner, Ralf & Gatzert, Nadine, 2013. "Estimating the basis risk of index-linked hedging strategies using multivariate extreme value theory," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4353-4367.
    9. 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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