Nonlife Ratemaking and Risk Management with Bayesian Additive Models for Location, Scale and Shape
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).
|Date of creation:||Oct 2013|
|Date of revision:|
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- Denuit, Michel & Lang, Stefan, 2004. "Non-life rate-making with Bayesian GAMs," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 627-647, December.
- Ludwig Fahrmeir & Stefan Lang, 2001. "Bayesian Semiparametric Regression Analysis of Multicategorical Time-Space Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 11-30, March.
- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, November.
- 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.
- 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.
- Stasinopoulos, D. Mikis & Rigby, Robert A., 2007. "Generalized Additive Models for Location Scale and Shape (GAMLSS) in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i07).
- Nadja Klein & Thomas Kneib & Stefan Lang, 2013. "Bayesian Structured Additive Distributional Regression," Working Papers 2013-23, Faculty of Economics and Statistics, University of Innsbruck.
- 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.
- 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.
- 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.
- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, November.
- 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.
- 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.
- 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.
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