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Paid-incurred chain claims reserving method

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  • Merz, Michael
  • Wüthrich, Mario V.

Abstract

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

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    1. Gogol, Daniel, 1993. "Using expected loss ratios in reserving," Insurance: Mathematics and Economics, Elsevier, vol. 12(3), pages 297-299, June.
    2. 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, Cambridge University Press, vol. 39(1), pages 275-306, May.
    3. Mack, Thomas, 1993. "Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 213-225, November.
    4. Gisler, Alois & Wüthrich, Mario V., 2008. "Credibility for the Chain Ladder Reserving Method," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 565-600, November.
    5. David Scollnik, 2001. "Actuarial Modeling with MCMC and BUGs," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(2), pages 96-124.
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    Citations

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    Cited by:

    1. Boratyńska, Agata, 2017. "Robust Bayesian estimation and prediction of reserves in exponential model with quadratic variance function," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 135-140.
    2. Eduardo Ramos-P'erez & Pablo J. Alonso-Gonz'alez & Jos'e Javier N'u~nez-Vel'azquez, 2022. "Mack-Net model: Blending Mack's model with Recurrent Neural Networks," Papers 2205.07334, arXiv.org.
    3. 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.
    4. Eduardo Ramos-P'erez & Pablo J. Alonso-Gonz'alez & Jos'e Javier N'u~nez-Vel'azquez, 2020. "Stochastic reserving with a stacked model based on a hybridized Artificial Neural Network," Papers 2008.07564, arXiv.org.
    5. Emmanuel Jordy Menvouta & Jolien Ponnet & Robin Van Oirbeek & Tim Verdonck, 2022. "mCube: Multinomial Micro-level reserving Model," Papers 2212.00101, arXiv.org.
    6. Benjamin Avanzi & Gregory Clive Taylor & Melantha Wang, 2021. "SPLICE: A Synthetic Paid Loss and Incurred Cost Experience Simulator," Papers 2109.04058, arXiv.org, revised Mar 2022.
    7. Peng Shi, 2017. "A Multivariate Analysis of Intercompany Loss Triangles," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(2), pages 717-737, June.
    8. 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.
    9. 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.
    10. Yixing Zhao & Rogemar Mamon & Heng Xiong, 2021. "Claim reserving for insurance contracts in line with the International Financial Reporting Standards 17: a new paid-incurred chain approach to risk adjustments," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-26, December.

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