Credibility and the Dirichlet process

Credibilists usually side-step the problem of specifying the structure function for a collective of risk experiences by finding certain projections in certain Hilbert spaces. These projections represent approximations to the Bayes rule. However, since both the credibility mean and credibility distribution function are proper Bayes relative to a Dirichlet process prior it is natural for the present paper to investigate the suitability of this process as a structure function. The proposed nonparametric models provide some increased insight into the credibility factor Z and the manual premium m; in particular, novel estimators for them are suggested.