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The connection between distortion risk measures and ordered weighted averaging operators

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  • Jaume Belles-Sampera

    ()
    (Faculty of Economics, University of Barcelona)

  • José M. Merigó

    ()
    (Faculty of Economics, University of Barcelona)

  • Montserrat Guillén

    ()
    (Faculty of Economics, University of Barcelona)

  • Miguel Santolino

    ()
    (Faculty of Economics, University of Barcelona)

Abstract

Distortion risk measures summarize the risk of a loss distribution by means of a single value. In fuzzy systems, the Ordered Weighted Averaging (OWA) and Weighted Ordered Weighted Averaging (WOWA) operators are used to aggregate a large number of fuzzy rules into a single value. We show that these concepts can be derived from the Choquet integral, and then the mathematical relationship between distortion risk measures and the OWA and WOWA operators for discrete and nite random variables is presented. This connection o ers a new interpretation of distortion risk measures and, in particular, Value-at-Risk and Tail Value-at-Risk can be understood from an aggregation operator perspective. The theoretical results are illustrated in an example and the degree of orness concept is discussed.

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Bibliographic Info

Paper provided by University of Barcelona, Research Institute of Applied Economics in its series IREA Working Papers with number 201201.

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Length: 31 pages
Date of creation: Jan 2012
Date of revision: Jan 2012
Handle: RePEc:ira:wpaper:201201

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Keywords: Fuzzy systems; Degree of orness; Risk quantification; Discrete random variable JEL classification:C02; C60;

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Cited by:
  1. Jaume Belles-Sampera & Montserrat Guillén & Miguel Santolino, 2013. "“Beyond Value-at-Risk: GlueVaR Distortion Risk Measures”," IREA Working Papers 201302, University of Barcelona, Research Institute of Applied Economics, revised Feb 2013.

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