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On Some Properties of Two Vector-Valued VaR and CTE Multivariate Risk Measures for Archimedean Copulas
Company: ASTIN Bulletin
Company Url: Click here to open
Year Of Publication: 2014
Month Of Publication: June
Resource Link: Click here to open
Pages: 21
Download Count: 0
View Count: 916
Comment Num: 0
Language: English
Source: article
Who Can Read: Free
Date: 6-22-2014
Publisher: Administrator
we derive integral formulas for the multivariate VaR and CTE Archimedean risk measures. We show that each component of the multivariate VaR and CTE functional vectors is an integral transform of the corresponding univariate VaR measures. For the class of Archimedean copulas, the marginal components of the CTE vector satisfy the following properties: positive homogeneity (PH), translation invariance (TI), monotonicity (MO), safety loading (SL) and VaR inequality (VIA). In case marginal risks satisfy the subadditivity (MSA) property, the marginal CTE components are also sub-additive and hitherto coherent risk measures in the usual sense. Moreover, the increasing risk (IR) or stop-loss order preserving property of the marginal CTE components holds for the class of bivariate Archimedean copulas. A counterexample to the (IR) property for the trivariate Clayton copula is included.
Hurlimann, Werner Sign in to follow this author
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