Nonparametric Bayesian Credibility

This paper introduces nonparametric Bayesian credibility without imposing
stringent parametric assumptions on claim distributions. We suppose that a claim
distribution associated with an unknown risk characteristic of a policyholder is an
unknown parameter vector with infinite dimension. In this way, we incorporate
the uncertainty of the functional form of the claim distribution associated with
the unknown risk characteristic in calculating credibility premiums. Using the
results of Ferguson (1973), formulas of the Bayesian credibility premiums are
obtained. The formula for the Bayesian credibility pure premium is a linear
combination of the overall mean and the sample mean of the claims. This
is consistent with the result in the classical credibility theory. We perform a
simulation study for the nonparametric Bayesian credibility pure premiums
and compare them with the corresponding Bühlmann credibility premiums.
Estimation results for the credibility premiums using Danish fire insurance loss
data are presented