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Title: The connection between distortion risk measures and ordered weighted averaging operators
Author: Belles Sampera, Jaume
Merigó Lindahl, José M.
Guillén, Montserrat
Santolino, Miguel
Keywords: Presa de decisions (Estadística)
Teoria d'operadors
Direcció d'empreses
Lògica matemàtica
Statistical decision
Operator theory
Industrial management
Mathematical logic
Issue Date: 2012
Publisher: Universitat de Barcelona. Institut de Recerca en Economia Aplicada Regional i Pública
Series/Report no: [WP E-IR12/01]
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.
Note: Reproducció del document publicat a:
It is part of: IREA – Working Papers, 2012, IR12/01
ISSN: 2014-1254
Appears in Collections:Documents de treball (Institut de Recerca en Economia Aplicada Regional i Pública (IREA))

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