Extreme value estimation of the conditional risk premium in reinsurance

In the paper we study the estimation of reinsurance premiums when the claim size is observed together with additional information in the form of random covariates. Using extreme value arguments, we propose an estimator for the risk premium conditional on a value for the covariate, and derive its asymptotic properties, after suitable normalization. The finite sample behavior is evaluated with a simulation experiment, and we apply the methodology to a dataset of automobile insurance claims from Australia.