IDEAS home Printed from https://ideas.repec.org/a/ags/reapec/50154.html
   My bibliography  Save this article

Risky Loss Distributions and Modeling the Loss Reserve Pay-out Tail

Author

Listed:
  • Cummins, J. David
  • McDonald, James B.
  • Merrill, Craig

Abstract

Although an extensive literature has developed on modeling the loss reserve runoff triangle, the estimation of severity distributions applicable to claims settled in specific cells of the runoff triangle has received little attention in the literature. This paper proposes the use of a very flexible probability density function, the generalized beta of the 2nd kind (GB2) to model severity distributions in the cells of the runoff triangle and illustrates the use of the GB2 based on a sample of nearly 500,000 products liability paid claims. The results show that the GB2 provides a significantly better fit to the severity data than conventional distributions such as the Weibull, Burr 12, and generalized gamma and that modeling severity by cell is important to avoid errors in estimating the riskiness of liability claims payments, especially at the longer lags.

Suggested Citation

  • Cummins, J. David & McDonald, James B. & Merrill, Craig, 2007. "Risky Loss Distributions and Modeling the Loss Reserve Pay-out Tail," Review of Applied Economics, Review of Applied Economics, vol. 3(1-2).
  • Handle: RePEc:ags:reapec:50154
    as

    Download full text from publisher

    File URL: http://purl.umn.edu/50154
    Download Restriction: no

    References listed on IDEAS

    as
    1. J. David Cummins & Richard D. Phillips & Stephen D. Smith, 1997. "Derivatives and corporate risk management: participation and volume decisions in the insurance industry," FRB Atlanta Working Paper 97-12, Federal Reserve Bank of Atlanta.
    2. Cummins, J. David & Dionne, Georges & McDonald, James B. & Pritchett, B. Michael, 1990. "Applications of the GB2 family of distributions in modeling insurance loss processes," Insurance: Mathematics and Economics, Elsevier, vol. 9(4), pages 257-272, December.
    3. McDonald, James B & Butler, Richard J, 1987. "Some Generalized Mixture Distributions with an Application to Unemployment Duration," The Review of Economics and Statistics, MIT Press, vol. 69(2), pages 232-240, May.
    4. David Cummins & Christopher Lewis & Richard Phillips, 1999. "Pricing Excess-of-Loss Reinsurance Contracts against Cat as trophic Loss," NBER Chapters,in: The Financing of Catastrophe Risk, pages 93-148 National Bureau of Economic Research, Inc.
    5. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-663, May.
    6. Mack, Thomas, 1991. "A Simple Parametric Model for Rating Automobile Insurance or Estimating IBNR Claims Reserves," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 21(01), pages 93-109, April.
    7. Bookstaber, Richard M & McDonald, James B, 1987. "A General Distribution for Describing Security Price Returns," The Journal of Business, University of Chicago Press, vol. 60(3), pages 401-424, July.
    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. Alice X. D. Dong & Jennifer S. K. Chan & Gareth W. Peters, 2014. "Risk Margin Quantile Function Via Parametric and Non-Parametric Bayesian Quantile Regression," Papers 1402.2492, arXiv.org.
    2. James Hansen & James McDonald & Panayiotis Theodossiou & Brad Larsen, 2010. "Partially Adaptive Econometric Methods For Regression and Classification," Computational Economics, Springer;Society for Computational Economics, vol. 36(2), pages 153-169, August.
    3. Dong, A.X.D. & Chan, J.S.K., 2013. "Bayesian analysis of loss reserving using dynamic models with generalized beta distribution," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 355-365.
    4. Li, Yunxian & Tang, Niansheng & Jiang, Xuejun, 2016. "Bayesian approaches for analyzing earthquake catastrophic risk," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 110-119.

    More about this item

    Keywords

    Loss distributions; loss reserves; generalized beta distribution; liability insurance; Risk and Uncertainty; C16; G22;

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • 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:ags:reapec:50154. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (AgEcon Search). General contact details of provider: http://www.lincoln.ac.nz/story11874.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.