Robust estimator of distortion risk premiums for heavy-tailed losses

TL;DR

This paper introduces a robust estimator for distortion risk premiums in heavy-tailed losses using the t-Hill tail index, demonstrating improved robustness over previous methods through theoretical analysis and simulations.

Contribution

It proposes a new robust estimator based on the t-Hill tail index for distortion risk premiums, with proven asymptotic normality under regular variation.

Findings

The new estimator is more robust than previous methods.

It performs well for both small and large samples.

The estimator's asymptotic normality is established.

Abstract

We use the so-called t-Hill tail index estimator proposed by Fabi\'an(2001), rather than Hill's one, to derive a robust estimator for the distortion risk premium of loss. 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.