Bühlmann credibility model with correlated risk parameters

Credibility theory is one of the tools to predict the amount of future claims by combining the experience of the claims in the past of a particular policyholder and external information, which is called manual rate, obtained from the experience of a large group of policyholders. One of the credibility theory that is widely used is Bühlmann credibility, which accommodates the heterogeneity of risk exposures, noted by unique risk parameters for each individual. However, Bühlmann credibility requires an assumption that the risk parameters are independent, which almost surely cannot be fulfilled by individuals living in the same area. Therefore, the Bühlmann credibility estimator with correlated risk parameters is formed by utilizing the orthogonal projection in Hilbert space. Also, the parameters included in the model are estimated. In addition, the standard Bühlmann credibility estimator and the Bühlmann credibility estimator assuming correlated risk parameters are compared to predict the amount of future claims based on data from a life insurance company. Comparing the root mean square error, the credibility estimator with correlated risk parameters is better in predicting the amount of future claim, meaning that the predicted amount of claim is closer to the original amount of claim. Also, as the correlation increases, the root mean square error becomes smaller. Moreover, the credibility estimator applied to the data that is partitioned based on the amount of past claims shows better performance than when applied to unpartitioned data.