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Paid-incurred chain claims reserving method


  • Merz, Michael
  • Wüthrich, Mario V.


We present a novel stochastic model for claims reserving that allows us to combine claims payments and incurred losses information. The main idea is to combine two claims reserving models (Hertig's (1985) model and Gogol's (1993) model ) leading to a log-normal paid-incurred chain (PIC) model. Using a Bayesian point of view for the parameter modelling we derive in this Bayesian PIC model the full predictive distribution of the outstanding loss liabilities. On the one hand, this allows for an analytical calculation of the claims reserves and the corresponding conditional mean square error of prediction. On the other hand, simulation algorithms provide any other statistics and risk measure on these claims reserves.

Suggested Citation

  • Merz, Michael & Wüthrich, Mario V., 2010. "Paid-incurred chain claims reserving method," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 568-579, June.
  • Handle: RePEc:eee:insuma:v:46:y:2010:i:3:p:568-579

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    References listed on IDEAS

    1. Gisler, Alois & Wüthrich, Mario V., 2008. "Credibility for the Chain Ladder Reserving Method," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 38(02), pages 565-600, November.
    2. Gogol, Daniel, 1993. "Using expected loss ratios in reserving," Insurance: Mathematics and Economics, Elsevier, vol. 12(3), pages 297-299, June.
    3. Bühlmann, Hans & De Felice, Massimo & Gisler, Alois & Moriconi, Franco & Wüthrich, Mario V., 2009. "Recursive Credibility Formula for Chain Ladder Factors and the Claims Development Result," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 39(01), pages 275-306, May.
    4. Mack, Thomas, 1993. "Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 23(02), pages 213-225, November.
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    Cited by:

    1. repec:bla:jrinsu:v:84:y:2017:i:2:p:717-737 is not listed on IDEAS
    2. Gareth W. Peters & Alice X. D. Dong & Robert Kohn, 2012. "A Copula Based Bayesian Approach for Paid-Incurred Claims Models for Non-Life Insurance Reserving," Papers 1210.3849,, revised Dec 2012.
    3. repec:eee:insuma:v:76:y:2017:i:c:p:135-140 is not listed on IDEAS
    4. Robert, Christian Y., 2013. "Market Value Margin calculations under the Cost of Capital approach within a Bayesian chain ladder framework," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 216-229.
    5. Pigeon, Mathieu & Antonio, Katrien & Denuit, Michel, 2014. "Individual loss reserving using paid–incurred data," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 121-131.
    6. Peters, Gareth W. & Dong, Alice X.D. & Kohn, Robert, 2014. "A copula based Bayesian approach for paid–incurred claims models for non-life insurance reserving," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 258-278.


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