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Model Uncertainty in Claims Reserving within Tweedie's Compound Poisson Models

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  • Peters, Gareth W.
  • Shevchenko, Pavel V.
  • Wüthrich, Mario V.

Abstract

In this paper we examine the claims reserving problem using Tweedie's compound Poisson model. We develop the maximum likelihood and Bayesian Markov chain Monte Carlo simulation approaches to fit the model and then compare the estimated models under different scenarios. The key point we demonstrate relates to the comparison of reserving quantities with and without model uncertainty incorporated into the prediction. We consider both the model selection problem and the model averaging solutions for the predicted reserves. As a part of this process we also consider the sub problem of variable selection to obtain a parsimonious representation of the model being fitted.

Suggested Citation

  • Peters, Gareth W. & Shevchenko, Pavel V. & Wüthrich, Mario V., 2009. "Model Uncertainty in Claims Reserving within Tweedie's Compound Poisson Models," ASTIN Bulletin, Cambridge University Press, vol. 39(1), pages 1-33, May.
    • Handle: RePEc:cup:astinb:v:39:y:2009:i:01:p:1-33_00
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    Citations

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    Cited by:

    1. Avanzi, Benjamin & Taylor, Greg & Vu, Phuong Anh & Wong, Bernard, 2020. "A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 50-71.
    2. 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.
    3. Pavel V. Shevchenko, 2010. "Implementing loss distribution approach for operational risk," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(3), pages 277-307, May.
    4. Suryo Adi Rakhmawan & Tahir Mahmood & Nasir Abbas & Muhammad Riaz, 2024. "Unifying mortality forecasting model: an investigation of the COM–Poisson distribution in the GAS model for improved projections," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(4), pages 800-826, October.
    5. Taylor, Greg, 2019. "A Cape Cod model for the exponential dispersion family," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 126-137.
    6. 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.
    7. Xiaolin Luo & Pavel V. Shevchenko, 2012. "Bayesian Model Choice of Grouped t-Copula," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 1097-1119, December.
    8. Alice X. D. Dong & Jennifer S. K. Chan & Gareth W. Peters, 2014. "Risk Margin Quantile Function Via Parametric and Non-Parametric Bayesian Quantile Regression," Papers 1402.2492, arXiv.org.
    9. Peters, Gareth W. & Shevchenko, Pavel V. & Young, Mark & Yip, Wendy, 2011. "Analytic loss distributional approach models for operational risk from the α-stable doubly stochastic compound processes and implications for capital allocation," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 565-579.
    10. Lally, Nathan & Hartman, Brian, 2018. "Estimating loss reserves using hierarchical Bayesian Gaussian process regression with input warping," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 124-140.
    11. Gian Paolo Clemente & Nino Savelli & Diego Zappa, 2019. "Modelling Outstanding Claims with Mixed Compound Processes in Insurance," International Business Research, Canadian Center of Science and Education, vol. 12(3), pages 123-138, March.
    12. Avanzi, Benjamin & Taylor, Greg & Vu, Phuong Anh & Wong, Bernard, 2016. "Stochastic loss reserving with dependence: A flexible multivariate Tweedie approach," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 63-78.
    13. Benjamin Avanzi & Gregory Clive Taylor & Phuong Anh Vu & Bernard Wong, 2020. "A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving," Papers 2004.06880, arXiv.org.
    14. Denuit, Michel & Trufin, Julien, 2016. "Beyond the Tweedie Reserving Model: The Collective Approach to Loss Development," LIDAM Discussion Papers ISBA 2016030, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. 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.
    16. Gareth W. Peters & Wilson Ye Chen & Richard H. Gerlach, 2016. "Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-Moments," Risks, MDPI, vol. 4(2), pages 1-41, May.

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