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

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  • 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, Lincoln University, Department of Financial and Business Systems, vol. 3(1-2), pages 1-23.
  • Handle: RePEc:ags:reapec:50154
    DOI: 10.22004/ag.econ.50154
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    References listed on IDEAS

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    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. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    6. Mack, Thomas, 1991. "A Simple Parametric Model for Rating Automobile Insurance or Estimating IBNR Claims Reserves," ASTIN Bulletin, Cambridge University Press, vol. 21(1), 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.
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    Cited by:

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    3. 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.
    4. 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.

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