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IR12-001_Belles-Sampera.pdf (702.88 KB)

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Document de treball

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2012

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cc-by-nc-nd, (c) Belles Sampera et al., 2012
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/58303

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

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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.

Matèries

Presa de decisions (Estadística), Teoria d'operadors, Direcció d'empreses, Lògica matemàtica

Matèries (anglès)

Statistical decision, Operator theory, Industrial management, Mathematical logic

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Documents de treball (Institut de Recerca en Economia Aplicada Regional i Pública (IREA))

Citació

BELLES SAMPERA, Jaume, MERIGÓ LINDAHL, José m., GUILLÉN, Montserrat, SANTOLINO, Miguel. The connection between distortion risk measures and ordered weighted averaging operators [WP]. _IREA – Working Papers_. 2012. Vol.  IR12/01. [consulta: 25 de gener de 2026]. ISSN: 2014-1254. [Disponible a: https://hdl.handle.net/2445/58303]

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