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Modelling catastrophe claims with left-truncated severity distributions (extended version)


  • Chernobai, Anna
  • Burnecki, Krzysztof
  • Rachev, Svetlozar
  • Trueck, Stefan
  • Weron, Rafal


In this paper, we present a procedure for consistent estimation of the severity and frequency distributions based on incomplete insurance data and demonstrate that ignoring the thresholds leads to a serious underestimation of the ruin probabilities. The event frequency is modelled with a non-homogeneous Poisson process with a sinusoidal intensity rate function. The choice of an adequate loss distribution is conducted via the in-sample goodness-of-fit procedures and forecasting, using classical and robust methodologies. This is an extended version of the article: Chernobai et al. (2006) Modelling catastrophe claims with left-truncated severity distributions, Computational Statistics 21(3-4): 537-555.

Suggested Citation

  • Chernobai, Anna & Burnecki, Krzysztof & Rachev, Svetlozar & Trueck, Stefan & Weron, Rafal, 2005. "Modelling catastrophe claims with left-truncated severity distributions (extended version)," MPRA Paper 10423, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:10423

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    References listed on IDEAS

    1. Burnecki, Krzysztof & Misiorek, Adam & Weron, Rafal, 2010. "Loss Distributions," MPRA Paper 22163, University Library of Munich, Germany.
    2. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501, June.
    3. Chernobai, Anna & Menn, Christian & Rachev, Svetlozar T. & Trück, Stefan, 2010. "Estimation of operational value-at-risk in the presence of minimum collection threshold: An empirical study," Working Paper Series in Economics 4, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
    4. Härdle, Wolfgang Karl & Burnecki, Krzysztof & Weron, Rafał, 2004. "Simulation of risk processes," Papers 2004,01, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    5. Krzysztof Burnecki & Wolfgang Hardle & Rafal Weron, 2003. "An introduction to simulation of risk processes," HSC Research Reports HSC/03/04, Hugo Steinhaus Center, Wroclaw University of Technology.
    6. Burnecki, Krzysztof & Kukla, Grzegorz & Weron, Rafał, 2000. "Property insurance loss distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(1), pages 269-278.
    7. L. Randall Wray & Stephanie Bell, 2004. "Introduction," Chapters,in: Credit and State Theories of Money, chapter 1 Edward Elgar Publishing.
    8. Knez, Peter J & Ready, Mark J, 1997. " On the Robustness of Size and Book-to-Market in Cross-Sectional Regressions," Journal of Finance, American Finance Association, vol. 52(4), pages 1355-1382, September.
    9. Michael Bierbrauer & Stefan Trueck & Rafal Weron, 2005. "Modeling electricity prices with regime switching models," Econometrics 0502005, EconWPA.
    10. Marco Bee, 2005. "On maximum likelihood estimation of operational loss distributions," Department of Economics Working Papers 0503, Department of Economics, University of Trento, Italia.
    11. Philippe Robert-Demontrond & R. Ringoot, 2004. "Introduction," Post-Print halshs-00081823, HAL.
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    Cited by:

    1. Rafal Weron, 2005. "Heavy tails and electricity prices," HSC Research Reports HSC/05/02, Hugo Steinhaus Center, Wroclaw University of Technology.
    2. Nowak, Piotr & Romaniuk, Maciej, 2013. "Pricing and simulations of catastrophe bonds," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 18-28.

    More about this item


    Natural Catastrophe; Property Insurance; Loss Distribution; Truncated Data; Ruin Probability;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General


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