Credibility Using Semiparametric Models With Adaptive Kernel

The goal of credibility theory is to estimate the future claim of a given risk. The most accurate estimator is predictive mean. If the conditional mean of losses given the risk parameter and the prior distribution of the risk parameter are known, true predictive mean can be easily obtained. However, risk parameter cannot be observed practically and it can be difficult to estimate its distribution. In this study, the structure function is estimated by using kernel density estimation with several bandwidth selection methods. For comparing the efficiences of these methods, a simulation study performed by using the data from a mixture of a lognormal conditional over a lognormal prior. The results shows that the adaptive bandwidth selection method performs better evidently for low claim severities.