Abstract

Credibility theory is a set of quantitative tools which allows insurers to perform prospective experience rating on a risk or group of risks in a heterogeneous portfolio. Credibility theory promotes a mechanism for the implementation of risk management strategies by differentiating between good and poor risks. It is used in the setting of rates for classification systems. Furthermore, application of credibility theory would also help to improve the ability of insurance companies to modify their price structure with the changing economic environment. Dannenburg [7] introduced a crossed classification credibility (CCC) model applicable to contracts that could be affected by many risk factors, that can not be modeled as nested or hierarchical relationships. In practice, the main problem in crossed classification credibility is the estimation of structure parameters. In a two-way CCC model, these parameters are the collective mean m , the time variance s 2 , and the variance components b (1) , b (2) , and b (12) . Dannenburg has already proposed estimators of these structure parameters. However, they have no known optimality property except unbiasedness. Goulet [24] proposed minimum variance unbiased (optimal) estimators for the mean and variance components. This thesis focuses on the implementation of the variance components estimators calculation. Analysis of algorithms and numerical evaluation procedures are studied to achieve computing efficiency. Through a simulation study, optimality of these estimators is then assessed in comparison to estimators proposed by Dannenburg [7]