Nonlife ratemaking and risk management with Bayesian generalized additive models for location,scale, and shape |
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Institution: | 1. University of Göttingen, Germany;2. Université Catholique de Louvain, Belgium;3. University of Innsbruck, Austria;1. Department of Statistics, Ewha Womans University, Seoul, Republic of Korea;2. Department of Statistics and Actuarial Science, Simon Fraser University, BC, Canada;3. Department of Mathematics and Statistics, Concordia University, Montreal, QC, Canada;1. School of Management, University of Science and Technology of China, Hefei, Anhui, China;2. College of Management, Shenzhen University, Shenzhen, Guangdong, China;3. Department of Information Systems, College of Business, City University of Hong Kong, China |
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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 key 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. New 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 linear effects as well as 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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Keywords: | Overdispersed count data Mixed Poisson regression Zero-inflated Poisson Negative binomial Zero-adjusted models MCMC Probabilistic forecasts |
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