Credibility Using Semiparametric Models

To use Bayesian analysis to model insurance losses, one usually chooses a parametric conditional loss distribution for each risk and a parametric prior distribution to describe how the conditional distributions vary across the risks. A criticism of this method is that the prior distribution can be difficult to choose and the resulting model may not represent the loss data very well. In this paper, we apply techniques from nonparametric density estimation to estimate the prior. We use the estimated model to calculate the predictive mean of future claims given past claims. We illustrate our method with simulated data from a mixture of a lognormal conditional over a lognormal prior and find that the estimated predictive mean is more accurate than the linear Bühlmann credibility estimator, even when we use a conditional that is not lognormal.