Extended Gini-type measures of risk and variability

TL;DR

This paper introduces the Extended Gini Shortfall, a new coherent risk measure that incorporates risk aversion and variability, with analytical computation methods and practical application.

Contribution

It extends Gini-type risk measures by integrating risk aversion within a coherent framework using Choquet integrals.

Findings

The measure is coherent and captures variability.

Analytic computation is feasible for common distributions.

Practical application demonstrates usefulness in risk management.

Abstract

The aim of this paper is to introduce a risk measure that extends the Gini-type measures of risk and variability, the Extended Gini Shortfall, by taking risk aversion into consideration. Our risk measure is coherent and catches variability, an important concept for risk management. The analysis is made under the Choquet integral representations framework. We expose results for analytic computation under well-known distribution functions. Furthermore, we provide a practical application.