Estimation of generalized tail distortion risk measures with applications in reinsurance

Abstract We present new estimators for generalized tail distortion (GTD) risk measures to assess extreme risks. Proposed estimators are based on the first‐order asymptotic expansions of the risk measure. They are simple to apply, and they are shown through simulation experiments to provide performance that is comparable or even better than that of existing estimation methods from the literature. A reinsurance premium principle based on the GTD risk measure is proposed. It is tested on car insurance claims data. We propose to use the GTD risk measure and the corresponding reinsurance premium to embed a safety loading in pricing, protecting against statistical uncertainty.