The connection between distortion risk measures and ordered weighted averaging operators

Jaume Belles-Sampera (), José M. Merigó, Montserrat Guillen and Miguel Santolino ()
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Jaume Belles-Sampera: Faculty of Economics, University of Barcelona
Miguel Santolino: Faculty of Economics, University of Barcelona

No 201201, IREA Working Papers from University of Barcelona, Research Institute of Applied Economics

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.

Keywords: Fuzzy systems; Degree of orness; Risk quantification; Discrete random variable JEL classification:C02,C60 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2012-01, Revised 2012-01
New Economics Papers: this item is included in nep-rmg and nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Journal Article: The connection between distortion risk measures and ordered weighted averaging operators (2013)
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