An estimating function approach to credibility theory

This thesis provides an alternative approach to the study of modern credibility theory: an estimating function approach. The theory of estimating functions is extended to study semiparametric Bayesian models. It is shown that previous credibility models, such as the Buhlmann-Straub model, the Jewell hierarchical model, the Hachemeister Bayesian regression model, and evolutionary credibility models can all be obtained easily within this approach. New models with higher order moments and changing conditional variance are suggested. The theory of estimating functions is also used to estimate parameters in the Buhlmann model and the newly suggested credibility model with ARCH variance structure. Numerical examples of simulations for each of the new methods are used for illustration and comparison.