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Nonlife Ratemaking and Risk Management with Bayesian Additive Models for Location, Scale and Shape

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  • Nadja Klein

    ()

  • Michel Denuit

    ()

  • Stefan Lang

    ()

  • Thomas Kneib

    ()

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    Abstract

    Generalized additive models for location, scale and shape define a flexible, semi-parametric class of regression models for analyzing insurance data in which the exponential family assumption for the response is relaxed. This approach allows the actuary to include risk factors not only in the mean but also in other parameters governing the claiming behavior, like the degree of residual heterogeneity or the no-claim probability. In this broader setting, the Negative Binomial regression with cell-specific heterogeneity and the zero-inflated Poisson regression with cell-specific additional probability mass at zero are applied to model claim frequencies. Models for claim severities that can be applied either per claim or aggregated per year are also presented. Bayesian inference is based on efficient Markov chain Monte Carlo simulation techniques and allows for the simultaneous estimation of possible nonlinear effects, spatial variations and interactions between risk factors within the data set. To illustrate the relevance of this approach, a detailed case study is proposed based on the Belgian motor insurance portfolio studied in Denuit and Lang (2004).

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    File URL: http://eeecon.uibk.ac.at/wopec2/repec/inn/wpaper/2013-24.pdf
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    Bibliographic Info

    Paper provided by Faculty of Economics and Statistics, University of Innsbruck in its series Working Papers with number 2013-24.

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    Length: 56 pages
    Date of creation: Oct 2013
    Date of revision:
    Handle: RePEc:inn:wpaper:2013-24

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    Related research

    Keywords: overdispersed count data; mixed Poisson regression; zero-inflated Poisson; Negative Binomial; zero-adjusted models; MCMC; probabilistic forecasts;

    This paper has been announced in the following NEP Reports:

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Ludwig Fahrmeir & Stefan Lang, 2001. "Bayesian Semiparametric Regression Analysis of Multicategorical Time-Space Data," Annals of the Institute of Statistical Mathematics, Springer, vol. 53(1), pages 11-30, March.
    2. Ludwig Fahrmeir & Stefan Lang, 2001. "Bayesian inference for generalized additive mixed models based on Markov random field priors," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(2), pages 201-220.
    3. D. Mikis Stasinopoulos & Robert A. Rigby, . "Generalized Additive Models for Location Scale and Shape (GAMLSS) in R," Journal of Statistical Software, American Statistical Association, vol. 23(i07).
    4. S. N. Wood, 2000. "Modelling and smoothing parameter estimation with multiple quadratic penalties," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 413-428.
    5. Denuit, Michel & Lang, Stefan, 2004. "Non-life rate-making with Bayesian GAMs," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 627-647, December.
    6. Nadja Klein & Thomas Kneib & Stefan Lang, 2013. "Bayesian Structured Additive Distributional Regression," Working Papers 2013-23, Faculty of Economics and Statistics, University of Innsbruck.
    7. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    8. X. Lin & D. Zhang, 1999. "Inference in generalized additive mixed modelsby using smoothing splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 381-400.
    9. Stefan Lang & Nikolaus Umlauf & Peter Wechselberger & Kenneth Harttgen & Thomas Kneib, 2012. "Multilevel structured additive regression," Working Papers 2012-07, Faculty of Economics and Statistics, University of Innsbruck.
    10. Simon N. Wood, 2003. "Thin plate regression splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 95-114.
    11. Nadja Klein & Thomas Kneib & Stefan Lang, 2013. "Bayesian generalized additive models for location, scale and shape for zero-inflated and overdispersed count data," Working Papers 2013-12, Faculty of Economics and Statistics, University of Innsbruck.
    12. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    13. Gneiting, Tilmann & Ranjan, Roopesh, 2011. "Comparing Density Forecasts Using Threshold- and Quantile-Weighted Scoring Rules," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 411-422.
    14. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
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