IDEAS home Printed from https://ideas.repec.org/p/wuu/wpaper/hsc0501.html
   My bibliography  Save this paper

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

Author

Listed:
  • Anna Chernobai
  • Krzysztof Burnecki
  • Svetlozar Rachev
  • Stefan Trueck
  • Rafal Weron

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.

Suggested Citation

  • Anna Chernobai & Krzysztof Burnecki & Svetlozar Rachev & Stefan Trueck & Rafal Weron, 2005. "Modeling catastrophe claims with left-truncated severity distributions (extended version)," HSC Research Reports HSC/05/01, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    • Handle: RePEc:wuu:wpaper:hsc0501
    as

    Download full text from publisher

    File URL: http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_05_01.pdf
    File Function: Original version, 2005
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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 Science and Technology, number hsbook0501, December.
    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 Management.
    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. 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.
    8. Michael Bierbrauer & Stefan Trueck & Rafal Weron, 2005. "Modeling electricity prices with regime switching models," Econometrics 0502005, University Library of Munich, Germany.
    9. Marco Bee, 2005. "On maximum likelihood estimation of operational loss distributions," Department of Economics Working Papers 0503, Department of Economics, University of Trento, Italia.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

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

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Weron, Rafał & Burnecki, Krzysztof, 2004. "Modeling the risk process in the XploRe computing environment," Papers 2004,08, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    2. Burnecki, Krzysztof & Janczura, Joanna & Weron, Rafal, 2010. "Building Loss Models," MPRA Paper 25492, University Library of Munich, Germany.
    3. Anna Chernobai & Krzysztof Burnecki & Svetlozar Rachev & Stefan Trück & Rafał Weron, 2006. "Modelling catastrophe claims with left-truncated severity distributions," Computational Statistics, Springer, vol. 21(3), pages 537-555, December.
    4. Rafal Weron, 2006. "Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach," HSC Books, Hugo Steinhaus Center, Wroclaw University of Science and Technology, number hsbook0601, December.
    5. 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).
    6. Wolfgang Karl Härdle & Brenda López Cabrera, 2010. "Calibrating CAT Bonds for Mexican Earthquakes," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(3), pages 625-650, September.
    7. Burnecki, Krzysztof & Misiorek, Adam & Weron, Rafal, 2010. "Loss Distributions," MPRA Paper 22163, University Library of Munich, Germany.
    8. repec:hum:wpaper:sfb649dp2007-037 is not listed on IDEAS
    9. Wolfgang Karl Härdle & Brenda López Cabrera, 2010. "Calibrating CAT Bonds for Mexican Earthquakes," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(3), pages 625-650, September.
    10. Rafał Weron, 2009. "Heavy-tails and regime-switching in electricity prices," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 457-473, July.
    11. Bernardi, Mauro & Maruotti, Antonello & Petrella, Lea, 2012. "Skew mixture models for loss distributions: A Bayesian approach," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 617-623.
    12. Rafal Weron, 2005. "Market price of risk implied by Asian-style electricity options," Econometrics 0502003, University Library of Munich, Germany.
    13. Weron, Rafał, 2014. "Electricity price forecasting: A review of the state-of-the-art with a look into the future," International Journal of Forecasting, Elsevier, vol. 30(4), pages 1030-1081.
    14. Joanna Janczura & Rafal Weron, 2012. "Inference for Markov-regime switching models of electricity spot prices," HSC Research Reports HSC/12/01, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    15. Wylomanska-, Agnieszka, 2010. "Measures of dependence for Ornstein-Uhlenbeck processes with tempered stable distribution," MPRA Paper 28535, University Library of Munich, Germany, revised 2010.
    16. Giuricich, Mario Nicoló & Burnecki, Krzysztof, 2019. "Modelling of left-truncated heavy-tailed data with application to catastrophe bond pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 498-513.
    17. Ma, Zong-Gang & Ma, Chao-Qun, 2013. "Pricing catastrophe risk bonds: A mixed approximation method," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 243-254.
    18. Janczura, Joanna & Weron, Rafal, 2010. "An empirical comparison of alternate regime-switching models for electricity spot prices," Energy Economics, Elsevier, vol. 32(5), pages 1059-1073, September.
    19. Cui, Yiran & del Baño Rollin, Sebastian & Germano, Guido, 2017. "Full and fast calibration of the Heston stochastic volatility model," European Journal of Operational Research, Elsevier, vol. 263(2), pages 625-638.
    20. Čížek, Pavel, 2008. "General Trimmed Estimation: Robust Approach To Nonlinear And Limited Dependent Variable Models," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1500-1529, December.
    21. Pouchkarev, I & Spronk, J. & Trinidad Segovia, J.E., 2004. "Dynamics of the Spanish Stock Market Through a Broadband View of the IBEX 35® index / Dinámica del mercado de capitales español a través de una visión amplia del índice IBEX 35®," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 22, pages 7-21, Abril.

    More about this item

    Keywords

    Natural catastrophe; Property insurance; Loss distribution; Truncated data; Ruin probability;
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wuu:wpaper:hsc0501. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Rafal Weron (email available below). General contact details of provider: https://edirc.repec.org/data/hspwrpl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.