Credibility modeling is a rate making process which allows actuaries to adjust the future premiums according to the past experience of a risk or group of risks. Many problems in actuarial science involve the mathematical models that can be used to forecast or predict insurance cost in the future, particularly the short-term future. Bühlmann (1967) 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. In the 1990s, with the existence of high-speed computers and statistical software packages, more sophisticated methodologies were introduced to this field. Klugman (1992) provided a Bayesian analysis to credibility theory by carefully choosing a parametric conditional loss distribution for each risk along with a parametric prior. Scollnik (1996) introduced Markov chain Monte Carlo (MCMC) methods to actuarial modeling, and Young (1997) used a semiparametric approach to estimate the structure function. 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 accounted for the correlated structure of the data. In this dissertation, 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 the relevant covariate information. The Bayesian modeling is carried out through sampling from a multivariate Gaussian prior, where the covariance structure is based on a thin-plate spline (Wahba, 1990). In addition, the model uses Markov chain Monte Carlo (MCMC) technique to compute the predictive distribution of the future claims based on the available data. In this approach, very little is assumed regarding the underlying model (signal); and we allow the data to “speak for itself”. An extensive data analysis is conducted to study the properties of the proposed estimator, and to compare the procedure against the existing techniques.
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