Bayesian Premium Rating with Latent Structure |
| |
Authors: | Xeni K Dimakos Arnoldo Frigessi Di Rattalma |
| |
Institution: | 1. Department of Mathematical Sciences , University of Wisconsin-Milwaukee , Milwaukee, WI, 53201, USA;2. Department of Mathematics , Indiana University , Bloomington, IN, 47405, USA;3. Department of Statistical and Actuarial Sciences , University of Western Ontario , London, Ontario, N6A 5B7, Canada |
| |
Abstract: | We propose a fully Bayesian approach to non-life risk premium rating, based on hierarchical models with latent variables for both claim frequency and claim size. Inference is based on the joint posterior distribution and is performed by Markov Chain Monte Carlo. Rather than plug-in point estimates of all unknown parameters, we take into account all sources of uncertainty simultaneously when the model is used to predict claims and estimate risk premiums. Several models are fitted to both a simulated dataset and a small portfolio regarding theft from cars. We show that interaction among latent variables can improve predictions significantly. We also investigate when interaction is not necessary. We compare our results with those obtained under a standard generalized linear model and show through numerical simulation that geographically located and spatially interacting latent variables can successfully compensate for missing covariates. However, when applied to the real portfolio data, the proposed models are not better than standard models due to the lack of spatial structure in the data. |
| |
Keywords: | Claim Frequency Claim Size Geopricing Generalized Linear Models Generalized Linear Mixed Models Hierarchical Models Latent Variables Markov Chain Monte Carlo Markov Random Fields Life Insurance Posterior Credibility Intervals Premium Rating Risk Premium Spatial Smoothing Theft From |
|
|