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The Geometric Chain-Ladder

Author

Listed:
  • D Kuang

    (Hiscox, London)

  • Bent Nielsen

    (Nuffield College, Oxford)

  • J P Nielsen

    (Cass Business School, City University London)

Abstract

The log normal reserving model is considered. The contribution of the paper is to derive explicit expressions for the maximum likelihood estimators. These are expressed in terms of development factors which are geometric averages. The distribution of the estimators is derived. It is shown that the analysis is invariant to traditional measures for exposure.

Suggested Citation

  • D Kuang & Bent Nielsen & J P Nielsen, 2013. "The Geometric Chain-Ladder," Economics Papers 2013-W11, Economics Group, Nuffield College, University of Oxford.
    • Handle: RePEc:nuf:econwp:1311
    as

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    File URL: http://www.nuffield.ox.ac.uk/economics/papers/2013/GeometricCL2013DP.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Mack, Thomas & Venter, Gary, 2000. "A comparison of stochastic models that reproduce chain ladder reserve estimates," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 101-107, February.
    3. D. Kuang & B. Nielsen & J. P. Nielsen, 2008. "Forecasting with the age-period-cohort model and the extended chain-ladder model," Biometrika, Biometrika Trust, vol. 95(4), pages 987-991.
    4. Di Kuang & Bent Nielsen & Jens Perch Nielsen, 2011. "Forecasting in an Extended Chain‐Ladder‐Type Model," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 78(2), pages 345-359, June.
    5. Verrall, R. J., 1991. "On the estimation of reserves from loglinear models," Insurance: Mathematics and Economics, Elsevier, vol. 10(1), pages 75-80, March.
    6. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(3), pages 443-518, August.
    7. Mack, Thomas, 1994. "Which stochastic model is underlying the chain ladder method?," Insurance: Mathematics and Economics, Elsevier, vol. 15(2-3), pages 133-138, December.
    8. D. Kuang & B. Nielsen & J. P. Nielsen, 2009. "Chain-Ladder as Maximum Likelihood Revisited," Economics Papers 2009-W08, Economics Group, Nuffield College, University of Oxford.
    9. Doray, Louis G., 1996. "UMVUE of the IBNR reserve in a lognormal linear regression model," Insurance: Mathematics and Economics, Elsevier, vol. 18(1), pages 43-57, May.
    10. England, Peter, 2002. "Addendum to "Analytic and bootstrap estimates of prediction errors in claims reserving"," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 461-466, December.
    11. Miranda, María Dolores Martínez & Nielsen, Bent & Nielsen, Jens Perch & Verrall, Richard, 2011. "Cash Flow Simulation for a Model of Outstanding Liabilities Based on Claim Amounts and Claim Numbers," ASTIN Bulletin, Cambridge University Press, vol. 41(1), pages 107-129, May.
    12. Kuang, D. & Nielsen, B. & Nielsen, J. P., 2009. "Chain-Ladder as Maximum Likelihood Revisited," Annals of Actuarial Science, Cambridge University Press, vol. 4(1), pages 105-121, March.
    13. Taylor, G. C. & Ashe, F. R., 1983. "Second moments of estimates of outstanding claims," Journal of Econometrics, Elsevier, vol. 23(1), pages 37-61, September.
    14. Verrall, R. J. & England, P. D., 2000. "Comments on: "A comparison of stochastic models that reproduce chain ladder reserve estimates", by Mack and Venter," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 109-111, February.
    15. Hertig, Joakim, 1985. "A Statistical Approach to IBNR-Reserves in Marine Reinsurance," ASTIN Bulletin, Cambridge University Press, vol. 15(2), pages 171-183, November.
    16. Taylor, Greg, 2003. "Chain Ladder Bias," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 313-330, November.
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    More about this item

    Keywords

    Arithmetic chain-ladder; geometric chain-ladder; canonical parameter; identification problem; maximum likelihood; log-normal model.;
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