Robust estimator of distortion risk premiums for heavy-tailed losses

We use the so called t-Hill estimator proposed by Fabi\'an(2001) to estimate the tail index of losses rather than the Hill estimator and to derive a new estimator for the distortion risk premium. We establish the asymptotic distribution of the new estimator. We illustrate their performance and the robustness for small and large sample size in a simulation study.