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New copulas based on general partitions-of-unity and their applications to risk management

100%
Pfeifer D., Tsatedem H. A., Mändle A., Girschig C.
Dependence Modeling
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2016
|
tom 4
|
nr 1
EN
We construct new multivariate copulas on the basis of a generalized infinite partition-of-unity approach. This approach allows, in contrast to finite partition-of-unity copulas, for tail-dependence as well as for asymmetry. A possibility of fitting such copulas to real data from quantitative risk management is also pointed out.
2
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On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators

100%
Di Bernardino E., Rullière D.
Dependence Modeling
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2013
|
tom 1
1-36
EN
We study the impact of certain transformations within the class of Archimedean copulas. We give some admissibility conditions for these transformations, and define some equivalence classes for both transformations and generators of Archimedean copulas. We extend the r-fold composition of the diagonal section of a copula, from r ∈ N to r ∈ R. This extension, coupled with results on equivalence classes, gives us new expressions of transformations and generators. Estimators deriving directly from these expressions are proposed and their convergence is investigated. We provide confidence bands for the estimated generators. Numerical illustrations show the empirical performance of these estimators.
3
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Extremal (in)dependence of a maximum autoregressive process

100%
Ferreira M.
Discussiones Mathematicae Probability and Statistics
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2013
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tom 33
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nr 1-2
47-64
EN
Maximum autoregressive processes like MARMA (Davis and Resnick, [5] 1989) or power MARMA (Ferreira and Canto e Castro, [12] 2008) have singular joint distributions, an unrealistic feature in most applications. To overcome this pitfall, absolute continuous versions were presented in Alpuim and Athayde [2] (1990) and Ferreira and Canto e Castro [14] (2010b), respectively. We consider an extended version of absolute continuous maximum autoregressive processes that accommodates both asymptotic tail dependence and independence. A full characterization of the bivariate lag-m tail dependence is presented. This will be useful in an adjustment procedure of the model to real data. An illustration with financial data is presented at the end.
4
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New copulas based on general partitions-of-unity and their applications to risk management (part II)

100%
Pfeifer D., Mändle A., Ragulina O.
Dependence Modeling
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2017
|
tom 5
|
nr 1
246-255
EN
We present a constructive and self-contained approach to data driven infinite partition-of-unity copulas that were recently introduced in the literature. In particular, we consider negative binomial and Poisson copulas and present a solution to the problem of fitting such copulas to highly asymmetric data in arbitrary dimensions.
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