Orlicz-Lorentz premia and distortion Haezendonck-Goovaerts risk measures

TL;DR

This paper introduces a new class of risk measures called distortion Haezendonck-Goovaerts risk measures, unifying existing measures and analyzing their properties in a broader risk space.

Contribution

It defines and studies a novel class of risk measures that combines distortion and Haezendonck-Goovaerts measures, extending their applicability and coherence properties.

Findings

The new risk measures are coherent under certain conditions.

They are defined on larger risk spaces than traditional measures.

The paper explores their risk-theoretic properties.

Abstract

In financial and actuarial research, distortion and Haezendonck-Goovaerts risk measures are attractive due to their strong properties. They have so far been treated separately. In this paper, following a suggestion by Goovaerts, Linders, Van Weert, and Tank, we introduce and study a new class of risk measure that encompasses the distortion and Haezendonck-Goovaerts risk measures, aptly called the distortion Haezendonck-Goovaerts risk measures. They will be defined on a larger space than the space of bounded risks. We provide situations where these new risk measures are coherent, and explore their risk theoretic properties.