Beyond Value‐at‐Risk: GlueVaR Distortion Risk Measures

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.

What attitudes to risk underlie distortion risk measure choices?

“…Our attention is focused on the characterization of the attitudes toward risk of the VaR, TVaR and a class of four-parameter distortion risk measures that are called GlueVaR (8) . The high flexibility of the GlueVaR distortion measures allows different specific attitudes to be reflected.…”

“…Many articles have recently examined risk measures based on either distortion functions (13,8,14) or generalizations of the quantiles (15,16) . The interplay between both of these two groups of risk measures has been examined (17,18) .…”

“…GlueVaR risk measures were introduced by Belles-Sampera et al (8) . These measures are defined by means of four parameters α, β, ω 1 and ω 2 , such that 0 < α ≤ β < 1,…”

Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle

“…Hence, the TVaR would appear to be a more powerful premium principle for assessing the actual risks faced by the reinsurance companies. For more detailed information about TVaR (AVaR) please refer to Belles-Sampera, et al [33].…”

GlueVaR risk measures in capital allocation applications

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AbstractBelles- Sampera et al (2014) GlueVaR risk measures generalize the traditional quantile-based approach to risk measurement, while a subfamily of these risk measures has been shown to satisfy the tail-subadditivity property. In this paper we show how GlueVaR risk measures can be implemented to solve problems of proportional capital allocation.

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