Ricerc@Sapienza

This paper concerns the study of the diversification effect involved in a portfolio of non-life policies priced via traditional
premium principles when individual pure premiums are calculated via Quantile Regression. Our aim is to use Quantile
Regression to estimate the individual conditional loss distribution given a vector of rating factors. To this aim, we make
a comparison of the outcomes obtained via Quantile Regression with the widely used industry standard method based on
generalized linear models. Then, considering a specific premium principle, we calculate individual pure premium by means
of a specific functional of the conditional loss distribution, the standard deviation. We determine the portfolio risk margin
according to the Solvency 2 framework and then we allocate it over each policy in a way consistent with his/her riskiness.
Indeed, considering a portfolio of heterogeneous policies, we determine the individual reduction of the safety loading, due to
the diversification, and we measure the risk contribution of each individual.