The connection between distortion risk measures and ordered weighted averaging operators

被引：33

作者：

Belles-Sampera, Jaume ^{[1
]}

Merigo, Jose M. ^{[2
,3
]}

Guillen, Montserrat ^{[1
]}

Santolino, Miguel ^{[1
]}

机构：

[1] Univ Barcelona, Riskctr IREA, Dept Econometr, E-08007 Barcelona, Spain

[2] Univ Barcelona, Riskctr IREA, Dept Business Adm, E-08007 Barcelona, Spain

[3] Univ Manchester, Manchester Business Sch, Manchester M13 9PL, Lancs, England

来源：

INSURANCE MATHEMATICS & ECONOMICS | 2013年 / 52卷 / 02期

关键词：

Fuzzy systems; Degree of omess; Risk quantification; Discrete random variable; FUZZY-LOGIC; PROSPECT-THEORY; DECISION; INSURANCE; AGGREGATION; PROBABILITY; UTILITY;

D O I：

10.1016/j.insmatheco.2013.02.008

中图分类号：

F [经济];

学科分类号：

02 ;

摘要：

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. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：411 / 420

页数：10

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