Beyond Value‐at‐Risk: GlueVaR Distortion Risk Measures

TLDR

The paper interprets GlueVaR in terms of risk attitudes and discusses its applicability to nonfinancial domains such as health, safety, environmental, and catastrophic risk management. The study proposes GlueVaR, a new family of distortion risk measures. GlueVaR is defined as a distortion risk measure that relates to value‑at‑risk and tail value‑at‑risk, and its properties are derived analytically. Closed‑form expressions for common distribution functions are derived, and some GlueVaR measures are shown to satisfy tail subadditivity.

Abstract

We propose a new family of risk measures, called GlueVaR, within the class of distortion risk measures. Analytical closed‐form expressions are shown for the most frequently used distribution functions in financial and insurance applications. The relationship between GlueVaR, value‐at‐risk, and tail value‐at‐risk is explained. Tail subadditivity is investigated and it is shown that some GlueVaR risk measures satisfy this property. An interpretation in terms of risk attitudes is provided and a discussion is given on the applicability in nonfinancial problems such as health, safety, environmental, or catastrophic risk management.