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A copula based Bayesian approach for paid–incurred claims models for non-life insurance reserving

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  • Peters, Gareth W.
  • Dong, Alice X.D.
  • Kohn, Robert

Abstract

Our article considers the class of recently developed stochastic models that combine claims payments and incurred losses information into a coherent reserving methodology. In particular, we develop a family of hierarchical Bayesian paid–incurred claims models, combining the claims reserving models of Hertig (1985) and Gogol (1993). In the process we extend the independent log-normal model of Merz and Wüthrich (2010) by incorporating different dependence structures using a Data-Augmented mixture Copula paid–incurred claims model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:59:y:2014:i:c:p:258-278
    DOI: 10.1016/j.insmatheco.2014.09.011
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    1. Peters, Gareth W. & Wüthrich, Mario V. & Shevchenko, Pavel V., 2010. "Chain ladder method: Bayesian bootstrap versus classical bootstrap," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 36-51, August.
    2. Gogol, Daniel, 1993. "Using expected loss ratios in reserving," Insurance: Mathematics and Economics, Elsevier, vol. 12(3), pages 297-299, June.
    3. Merz, Michael & Wüthrich, Mario V., 2010. "Paid-incurred chain claims reserving method," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 568-579, June.
    4. 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.
    5. Yanwei Zhang & Vanja Dukic, 2013. "Predicting Multivariate Insurance Loss Payments Under the Bayesian Copula Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 891-919, December.
    6. Hofert, Marius & Mächler, Martin & McNeil, Alexander J., 2012. "Likelihood inference for Archimedean copulas in high dimensions under known margins," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 133-150.
    7. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    8. Gareth W. Peters & Mario V. Wuthrich & Pavel V. Shevchenko, 2010. "Chain ladder method: Bayesian bootstrap versus classical bootstrap," Papers 1004.2548, arXiv.org.
    9. Aleksey Min & Claudia Czado, 2010. "Bayesian Inference for Multivariate Copulas Using Pair-Copula Constructions," Journal of Financial Econometrics, Oxford University Press, vol. 8(4), pages 511-546, Fall.
    10. Hertig, Joakim, 1985. "A Statistical Approach to IBNR-Reserves in Marine Reinsurance," ASTIN Bulletin, Cambridge University Press, vol. 15(2), pages 171-183, November.
    11. Paul Embrechts, 2009. "Copulas: A Personal View," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 639-650, September.
    12. Happ, Sebastian & Wüthrich, Mario V., 2013. "Paid-Incurred Chain Reserving Method With Dependence Modeling," ASTIN Bulletin, Cambridge University Press, vol. 43(1), pages 1-20, January.
    13. Gareth W. Peters & Balakrishnan Kannan & Ben Lasscock & Chris Mellen, 2010. "Model Selection and Adaptive Markov chain Monte Carlo for Bayesian Cointegrated VAR model," Papers 1004.3830, arXiv.org.
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    Cited by:

    1. Himchan Jeong & Dipak Dey, 2020. "Application of a Vine Copula for Multi-Line Insurance Reserving," Risks, MDPI, vol. 8(4), pages 1-23, October.
    2. Efstathios Panayi & Gareth W. Peters, 2015. "Stochastic simulation framework for the limit order book using liquidity-motivated agents," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(02), pages 1-52.
    3. Fersini, Paola & Melisi, Giuseppe, 2016. "Stochastic model to evaluate the fair value of motor third-party liability under the direct reimbursement scheme and quantification of the capital requirement in a Solvency II perspective," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 27-44.
    4. Ames, Matthew & Bagnarosa, Guillaume & Peters, Gareth W., 2017. "Violations of uncovered interest rate parity and international exchange rate dependences," Journal of International Money and Finance, Elsevier, vol. 73(PA), pages 162-187.
    5. Jan Barlak & Matus Bakon & Martin Rovnak & Martina Mokrisova, 2022. "Heat Equation as a Tool for Outliers Mitigation in Run-Off Triangles for Valuing the Technical Provisions in Non-Life Insurance Business," Risks, MDPI, vol. 10(9), pages 1-17, August.
    6. Efstathios Panayi & Gareth Peters, 2015. "Stochastic simulation framework for the Limit Order Book using liquidity motivated agents," Papers 1501.02447, arXiv.org, revised Jan 2015.
    7. 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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