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European Actuarial Journal

, Volume 8, Issue 2, pp 437–460 | Cite as

Matching tower information with piecewise Pareto

  • Ulrich RiegelEmail author
Original Research Paper
  • 109 Downloads

Abstract

Pricing tools for non-proportional reinsurance treaties often only provide layer prices, but no layer-independent collective risk model. There are, however, situations where such a layer-independent model is needed. Examples are large loss and catastrophe loss models for proportional reinsurance treaties. We show that the expected losses of a tower of reinsurance layers can always be matched using a piecewise Pareto distributed severity and provide an algorithm that can be used to convert layer information into a layer-independent collective risk model.

Keywords

Pareto distribution Reinsurance pricing Collective risk model 

Notes

Acknowledgements

I would like to thank the anonymous referee for his constructive comments which helped to improve the presentation of the paper substantially.

References

  1. 1.
    Albrecher H, Beirlant J, Teugels JL (2017) Reinsurance: actuarial and statistical aspects. Wiley, OxfordCrossRefGoogle Scholar
  2. 2.
    Fackler M (2013) Reinventing Pareto: fits for both small and large losses. ASTIN Colloquium Den Haag. http://www.actuaries.org/ASTIN/Colloquia/Hague/Papers/Fackler.pdf. Accessed 24 June 2018
  3. 3.
    Johnson NL, Kotz S (1970) Continuous univariate distributions-I. Houghton Mifflin Co/Wiley, New YorkzbMATHGoogle Scholar
  4. 4.
    Hannemann M et al (2007) Glossary of reinsurance terms. Kölnische Rückversicherungs-Gesellschaft AG, KölnGoogle Scholar
  5. 5.
    Kaas R, Goovaerts M, Dhaene J, Denuit M (2001) Modern actuarial risk theory. Kluwer Academic Publishers, BostonzbMATHGoogle Scholar
  6. 6.
    Klugman S, Panjer HH, Wilmot G (2008) Loss models: from data to decisions. Wiley, HobokenCrossRefGoogle Scholar
  7. 7.
    Liebwein P (2000) Klassische und moderne Formen der Rückversicherung. VVW, KarlsruheGoogle Scholar
  8. 8.
    Mack Th (2002) Schadenversicherungsmathematik. VVW, KarlsruheGoogle Scholar
  9. 9.
    Philbrick SW (1985) A practical guide to the single parameter pareto distribution. PCAS LXXII:44–84Google Scholar
  10. 10.
    Rytgaard M (1990) Estimation in the Pareto distribution. ASTIN Bull 20(2):201–216CrossRefGoogle Scholar
  11. 11.
    Riegel U (2008) Generalizations of common ILF models. Blätter der DGVFM 29:45–71MathSciNetCrossRefGoogle Scholar
  12. 12.
    Schmutz M, Doerr RR (1998) Das Pareto-Modell in der Sach-Rückversicherung. Formeln und Anwendungen. Swiss Re Publications, ZürichGoogle Scholar
  13. 13.
    Scollnik DPA (2007) On composite Lognormal–Pareto models. Scand Actuar J 1:20–33MathSciNetCrossRefGoogle Scholar
  14. 14.
    Scollnik DPA, Sun C (2012) Modeling with Weibull–Pareto models. NAAJ 16(1):260–272MathSciNetzbMATHGoogle Scholar

Copyright information

© EAJ Association 2018

Authors and Affiliations

  1. 1.Munich Reinsurance CompanyMunichGermany

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