Tail Dependence for Heavy-Tailed Scale Mixtures of Multivariate Distributions

Li, Haijun; Sun, Yannan

doi:10.1017/s0021900200006057

Cited by 14 publications

(13 citation statements)

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“…It was shown in [14] that tail dependence functions {b * S (w i , i ∈ S; C S )} and the exponent function a * (w; C) are uniquely determined from one to another. In fact, the detailed relations between the intensity measure µ and tail dependence function b * have been established in [19], and in particular,…”

Section: Bounds For Tail Risks Via Tail Dependence Functionsmentioning

confidence: 99%

Tail Risk of Multivariate Regular Variation

Joe

2010

Methodol Comput Appl Probab

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Tail risk refers to the risk associated with extreme values and is often affected by extremal dependence among multivariate extremes. Multivariate tail risk, as measured by a coherent risk measure of tail conditional expectation, is analyzed for multivariate regularly varying distributions. Asymptotic expressions for tail risk are established in terms of the intensity measure that characterizes multivariate regular variation. Tractable bounds for tail risk are derived in terms of the tail dependence function that describes extremal dependence. Various examples involving Archimedean copulas are presented to illustrate the results and quality of the bounds.

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Section: Bounds For Tail Risks Via Tail Dependence Functionsmentioning

confidence: 99%

Tail Risk of Multivariate Regular Variation

Joe

2010

Methodol Comput Appl Probab

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“…Schmidt [27] showed that bivariate elliptical distributions possess the tail dependence property if the tail of their generating random variable is regularly varying. The explicit expressions of the orthant tail dependence for multivariate Marshall-Olkin distributions have been derived in [17], and the moment-based formulas for multivariate tail dependence of scale mixtures of multivariate distributions, such as multivariate t-distributions, have been established in [3,18]. The use of (1.5) to study the contagion risk among 25 European and US banks is reported in [6].…”

Section: Theorem 11 a Distribution G Is An Mev Distribution With Stmentioning

confidence: 99%

Orthant tail dependence of multivariate extreme value distributions

2009

Journal of Multivariate Analysis

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a b s t r a c tThe orthant tail dependence describes the relative deviation of upper-(or lower-) orthant tail probabilities of a random vector from similar orthant tail probabilities of a subset of its components, and can be used in the study of dependence among extreme values. Using the conditional approach, this paper examines the extremal dependence properties of multivariate extreme value distributions and their scale mixtures, and derives the explicit expressions of orthant tail dependence parameters for these distributions. Properties of the tail dependence parameters, including their relations with other extremal dependence measures used in the literature, are discussed. Various examples involving multivariate exponential, multivariate logistic distributions and copulas of Archimedean type are presented to illustrate the results.

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“…and [31,18,25] further studied the properties of the tail dependence function and their applications for multivariate t copulas, vine copulas and heavy-tailed scale mixtures of multivariate distributions, respectively. We refer to the above papers for details and properties of tail dependence functions.…”

Section: Introductionmentioning

confidence: 99%