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The Geometric Chain-Ladder

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Author Info

  • 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.

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File URL: http://www.nuffield.ox.ac.uk/economics/papers/2013/GeometricCL2013DP.pdf
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Bibliographic Info

Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2013-W11.

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Length: 24 pages
Date of creation: 01 Jul 2013
Date of revision:
Handle: RePEc:nuf:econwp:1311

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Web page: http://www.nuff.ox.ac.uk/economics/

Related research

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

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References

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  1. D. Kuang & Bent Nielsen & J. P. Nielsen, 2008. "Forecasting with the age-period-cohort model and the extended chain-ladder model," Economics Papers 2008-W09, Economics Group, Nuffield College, University of Oxford.
  2. Verrall, R. J., 1991. "On the estimation of reserves from loglinear models," Insurance: Mathematics and Economics, Elsevier, vol. 10(1), pages 75-80, March.
  3. Bent Nielsen & D. Kuang and J.P. Nielsen, 2009. "Chain-Ladder as Maximum Likelihood Revisited," Economics Series Working Papers 2009-W08, University of Oxford, Department of Economics.
  4. 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.
  5. Bent Nielsen & Di Kuang and Jens Perch Nielsen, 2010. "Forecasting in an extended chain-ladder-type model," Economics Series Working Papers 2010-W05, University of Oxford, Department of Economics.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
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