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Model uncertainty in claims reserving within Tweedie's compound Poisson models

Author

Listed:
  • Gareth W. Peters
  • Pavel V. Shevchenko
  • Mario V. Wuthrich

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

  • Gareth W. Peters & Pavel V. Shevchenko & Mario V. Wuthrich, 2009. "Model uncertainty in claims reserving within Tweedie's compound Poisson models," Papers 0904.1483, arXiv.org.
  • Handle: RePEc:arx:papers:0904.1483
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    File URL: http://arxiv.org/pdf/0904.1483
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    References listed on IDEAS

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    1. Congdon, Peter, 2006. "Bayesian model choice based on Monte Carlo estimates of posterior model probabilities," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 346-357, January.
    2. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(03), pages 443-518, August.
    3. Cairns, Andrew J. G., 2000. "A discussion of parameter and model uncertainty in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 27(3), pages 313-330, December.
    4. Smyth, Gordon K. & Jørgensen, Bent, 2002. "Fitting Tweedie's Compound Poisson Model to Insurance Claims Data: Dispersion Modelling," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 32(01), pages 143-157, May.
    5. Rosenthal, Jeffrey S., 2007. "AMCMC: An R interface for adaptive MCMC," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5467-5470, August.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Gareth W. Peters & Wilson Y. Chen & Richard H. Gerlach, 2016. "Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-moments," Papers 1603.01041, arXiv.org.
    4. 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.
    5. repec:bla:jrinsu:v:84:y:2017:i:2:p:717-737 is not listed on IDEAS
    6. 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.
    7. 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, Open Access Journal, vol. 4(2), pages 1-41, May.
    8. repec:gam:jrisks:v:4:y:2016:i:2:p:14:d:70470 is not listed on IDEAS
    9. 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.
    10. repec:eee:insuma:v:76:y:2017:i:c:p:135-140 is not listed on IDEAS

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