Nonlife Ratemaking and Risk Management with Bayesian Additive Models for Location, Scale and Shape
AbstractGeneralized 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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Bibliographic InfoPaper provided by Faculty of Economics and Statistics, University of Innsbruck in its series Working Papers with number 2013-24.
Length: 56 pages
Date of creation: Oct 2013
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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:
- NEP-ALL-2013-10-18 (All new papers)
- NEP-ECM-2013-10-18 (Econometrics)
- NEP-FOR-2013-10-18 (Forecasting)
- NEP-RMG-2013-10-18 (Risk Management)
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