Credibility Modeling via Spline Nonparametric Regression

Credibility modeling is a rate making process which allows actuaries to adjust future premiums according to the past experience of a risk or group of risks. Current methods in credibility theory often rely on parametric models. Buhlmann developed an approach based on the best linear approximation, which leads to an estimator that is a linear combination of current observations and past records. During the last decade, the existence of high speed computers and statistical software packages allowed the introduction of more sophisticated methodologies. Some of these techniques are based on Markov Chain Monte Carlo (MCMC) approach to Bayesian inference, which requires extensive computations. However, very few of these methods made use of the additional covariate information related to the risk, or group of risks; and at the same time account for the correlated structure in the data. In this paper, we consider a Bayesian nonparametric approach to the problem of risk modeling. The model incorporates past and present observations related to the risk, as well as relevant covariate information. The Bayesian modeling is carried out by sampling from a multivariate Gaussian prior, where the covariance structure is based on a thin-plate spline. The model uses MCMC technique to compute the predictive distribution of the future claims based on the available data. Extensive data analysis is conducted to study the properties of the proposed estimator, and compare against the existing techniques.