Paths and Indices of Maximal Tail Dependence

Furman, Edward; Su, Jianxi; Zitikis, Ričardas

doi:10.1017/asb.2015.10

Cited by 21 publications

(44 citation statements)

References 29 publications

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“…More specifically, Furman et al (2015) claim and elucidate with numerous examples that as measures (21) and (22) Then the path (ϕ(u), u 2 /ϕ(u)) 0≤u≤1 is admissible whenever the function ϕ is admissible. In addition, we denote by A the set of all admissible functions ϕ.…”

Section: Theoretical Considerationsmentioning

confidence: 97%

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On a Multiplicative Multivariate Gamma Distribution with Applications in Insurance

Semenikhine

Furman

2018

Risks

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Abstract:One way to formulate a multivariate probability distribution with dependent univariate margins distributed gamma is by using the closure under convolutions property. This direction yields an additive background risk model, and it has been very well-studied. An alternative way to accomplish the same task is via an application of the Bernstein-Widder theorem with respect to a shifted inverse Beta probability density function. This way, which leads to an arguably equally popular multiplicative background risk model (MBRM), has been by far less investigated. In this paper, we reintroduce the multiplicative multivariate gamma (MMG) distribution in the most general form, and we explore its various properties thoroughly. Specifically, we study the links to the MBRM, employ the machinery of divided differences to derive the distribution of the aggregate risk random variable explicitly, look into the corresponding copula function and the measures of nonlinear correlation associated with it, and, last but not least, determine the measures of maximal tail dependence. Our main message is that the MMG distribution is (1) very intuitive and easy to communicate, (2) remarkably tractable, and (3) possesses rich dependence and tail dependence characteristics. Hence, the MMG distribution should be given serious considerations when modelling dependent risks.

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Section: Theoretical Considerationsmentioning

confidence: 97%

“…Lemma 3 (Furman et al 2015). For an Archimedean copula with generator φ, if x ∂ ∂x φ −1 (x) is increasing on x ∈ (0, 1), then the path of maximal dependence coincides with the main diagonal.…”

Section: Theoretical Considerationsmentioning

confidence: 99%

On a Multiplicative Multivariate Gamma Distribution with Applications in Insurance

Semenikhine

Furman

2018

Risks

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“…A discussion of the properties and disadvantages of these indices in the classification of extreme events is presented in refs. [7,8]. Plots of a mixture copula of Gumbel ( 1 = 1.5) and Clayton( 2 = 1) with = 0.5 on the left side and = 0.2 on the right side from those of multivariate normal models.…”

Section: Choice Of the Mixture In The Classification Process And Its mentioning

confidence: 99%

Dissimilarity measure for ranking data via mixture of copulae*

Bonanomi

Ruscone

Osmetti

2019

Statistical Analysis

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We define a new distance measure for ranking data using a mixture of copula functions. Our distance measure evaluates the dissimilarity of subjects' ranking preferences to segment them via hierarchical cluster analysis. The proposed distance measure builds upon Spearman grade correlation coefficient on a copula transformation of rank denoting the level of importance assigned by subjects on the classification of k objects. These mixtures of copulae enable flexible modeling of the different types of dependence structures found in data and the consideration of various circumstances in the classification process. For example, by using mixtures of copulae with lower and upper tail dependence, we can emphasize the agreement on extreme ranks when they are considered important.

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“…We next formally introduce measures of maximal tail dependence. To this end, we heavily borrow from Furman et al (2015). Then the path (ϕ(u), u 2 /ϕ(u)) 0≤u≤1 is admissible whenever the function ϕ is admissible.…”

Section: Measures Of Maximal Tail Dependencementioning

confidence: 99%

Multiple risk factor dependence structures: Copulas and related properties

Furman

2017

Insurance: Mathematics and Economics

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Abstract. Copulas have become an important tool in the modern best practice Enterprise Risk Management, often supplanting other approaches to modelling stochastic dependence. However, choosing the 'right' copula is not an easy task, and the temptation to prefer a tractable rather than a meaningful candidate from the encompassing copulas toolbox is strong. The ubiquitous applications of the Gaussian copula is just one illuminating example.Speaking generally, a 'good' copula should conform to the problem at hand, allow for asymmetry in the domain of definition and exhibit some extent of tail dependence. In this paper we introduce and study a new class of Multiple Risk Factor (MRF) copula functions, which we show are exactly such. Namely, the MRF copulas (1) arise from a number of meaningful default risk specifications with stochastic default barriers, (2) are in general non-exchangeable and (3) possess a variety of tail dependences. That being said, the MRF copulas turn out to be surprisingly tractable analytically.

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Paths and Indices of Maximal Tail Dependence

Cited by 21 publications

References 29 publications

On a Multiplicative Multivariate Gamma Distribution with Applications in Insurance

On a Multiplicative Multivariate Gamma Distribution with Applications in Insurance

Dissimilarity measure for ranking data via mixture of copulae*

Multiple risk factor dependence structures: Copulas and related properties

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