Distortion risk measures for sums of dependent losses

TL;DR

This paper introduces two coherent distortion risk measures for sums of dependent risks, accounting for fluctuations and correlations, by distorting either the survival function alone or both the survival function and dependence structure.

Contribution

It proposes novel coherent risk measures that incorporate dependence and fluctuations in sums of dependent risks using copulas and survival functions.

Findings

Two distinct approaches for distortion risk measures are proposed.

The measures account for dependence via copulas.

The methods preserve coherence of risk measures.

Abstract

We discuss two distinct approaches, for distorting risk measures of sums of dependent random variables, which preserve the property of coherence. The first, based on distorted expectations, operates on the survival function of the sum. The second, simultaneously applies the distortion on the survival function of the sum and the dependence structure of risks, represented by copulas. Our goal is to propose risk measures that take into account the fluctuations of losses and possible correlations between risk components.