The connection between distortion risk measures and ordered weighted averaging operators

Jaume Belles-Sampera, José M. Merigó, Montserrat Guillen and Miguel Santolino

Insurance: Mathematics and Economics, 2013, vol. 52, issue 2, 411-420

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 finite random variables is presented. This connection offers 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.

Keywords: Fuzzy systems; Degree of orness; Risk quantification; Discrete random variable (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (12)

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Working Paper: The connection between distortion risk measures and ordered weighted averaging operators (2012)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:52:y:2013:i:2:p:411-420

DOI: 10.1016/j.insmatheco.2013.02.008

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