  The risk premium of a policy is the sum of the pure premium and the risk
loading. In the classification ratemaking process, generalized linear models
are usually used to calculate pure premiums, and various premium principles are
applied to derive the risk loadings. No matter which premium principle is used,
some risk loading parameters should be given in advance subjectively. To
overcome this subjective problem and calculate the risk premium more reasonably
and objectively, we propose a top-down method to calculate these risk loading
parameters. First, we implement the bootstrap method to calculate the total
risk premium of the portfolio. Then, under the constraint that the portfolio's
total risk premium should equal the sum of the risk premiums of each policy,
the risk loading parameters are determined. During this process, besides using
generalized linear models, three kinds of quantile regression models are also
applied, namely, traditional quantile regression model, fully parametric
quantile regression model, and quantile regression model with coefficient
functions. The empirical result shows that the risk premiums calculated by the
method proposed in this study can reasonably differentiate the heterogeneity of
different risk classes.
