The connection between distortion risk measures and ordered weighted averaging operators [WP]

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RECERCAT Home > Universitat de Barcelona > Institut de Recerca en Economia Aplicada Regional i Pública (IREA) > Documents de treball (Institut de Recerca en Economia Aplicada Regional i Pública (IREA)) > View document

To access the full text documents, please follow this link: http://hdl.handle.net/2445/58303

dc.contributor.author	Belles Sampera, Jaume
dc.contributor.author	Merigó Lindahl, José M.
dc.contributor.author	Guillén, Montserrat
dc.contributor.author	Santolino, Miguel
dc.date	2014-10-08T11:10:32Z
dc.date	2014-10-08T11:10:32Z
dc.date	2012
dc.date	2014-10-08T11:10:33Z
dc.identifier.citation	2014-1254
dc.identifier.uri	http://hdl.handle.net/2445/58303
dc.format	31 p.
dc.format	application/pdf
dc.language.iso	eng
dc.publisher	Universitat de Barcelona. Institut de Recerca en Economia Aplicada Regional i Pública
dc.relation	Reproducció del document publicat a: http://www.ub.edu/irea/working_papers/2012/201201.pdf
dc.relation	IREA – Working Papers, 2012, IR12/01
dc.relation	[WP E-IR12/01]
dc.rights	cc-by-nc-nd, (c) Belles Sampera et al., 2012
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/
dc.subject	Presa de decisions (Estadística)
dc.subject	Teoria d'operadors
dc.subject	Direcció d'empreses
dc.subject	Lògica matemàtica
dc.subject	Statistical decision
dc.subject	Operator theory
dc.subject	Industrial management
dc.subject	Mathematical logic
dc.title	The connection between distortion risk measures and ordered weighted averaging operators [WP]
dc.type	info:eu-repo/semantics/workingPaper
dc.description.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.

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