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

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

Abstract

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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 10423.

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Date of creation: 2005
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Handle: RePEc:pra:mprapa:10423

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Related research

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

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References

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  1. 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 1355-82, September.
  2. 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.
  3. 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.
  4. Michael Bierbrauer & Stefan Trueck & Rafal Weron, 2005. "Modeling electricity prices with regime switching models," Econometrics 0502005, EconWPA.
  5. Burnecki, Krzysztof & Misiorek, Adam & Weron, Rafal, 2010. "Loss Distributions," MPRA Paper 22163, University Library of Munich, Germany.
  6. Marco Bee, 2005. "On maximum likelihood estimation of operational loss distributions," Department of Economics Working Papers 0503, Department of Economics, University of Trento, Italia.
  7. Krzysztof Burnecki & Grzegorz Kukla & Rafal Weron, 2000. "Property insurance loss distributions," HSC Research Reports HSC/00/03, Hugo Steinhaus Center, Wroclaw University of Technology.
  8. Härdle, Wolfgang Karl & Burnecki, Krzysztof & Weron, Rafał, 2004. "Simulation of risk processes," Papers 2004,01, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
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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.

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