Robust estimator of distortion risk premiums for heavy-tailed losses

Abstract

We use the so-called t-Hill tail index estimator proposed by Fabian (2001), rather than Hill's one, to derive a robust estimator for the distortion risk premium of losses. Under the second-order condition of regular variation, we establish its asymptotic normality. By simulation study, we show that this new estimator is more robust than of Necir and Meraghni (2009) both for small and large samples.

Keywords: Distortion risk premiums; Extreme values; Tail; Robustness