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Beyond Value-at-Risk: GlueVaR Distortion Risk Measures

Authors

  • Jaume Belles-Sampera,

    1. Department of Econometrics, Riskcenter-IREA, University of Barcelona, Barcelona, Spain
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  • Montserrat Guillén,

    1. Department of Econometrics, Riskcenter-IREA, University of Barcelona, Barcelona, Spain
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  • Miguel Santolino

    Corresponding author
    1. Department of Econometrics, Riskcenter-IREA, University of Barcelona, Barcelona, Spain
    • Address correspondence to: Miguel Santolino, Department of Econometrics, Riskcenter-IREA, University of Barcelona, Av. Diagonal, 690, 08034 Barcelona, Spain; tel: +34 934 020 484; msantolino@ub.edu.

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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.

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