Modeling defaults with nested Archimedean copulas

2010 ◽  
Vol 31 (2) ◽  
pp. 213-224 ◽  
Author(s):  
Marius Hofert
Keyword(s):  
Archimedean Copulas

Extreme Value Theory and Archimedean Copulas

2004 ◽  
Vol 2004 (3) ◽  
pp. 211-228 ◽  
Author(s):  
Mario V. Wüthrich
Keyword(s):  
Extreme Value Theory ◽  
Value Theory ◽  
Extreme Value ◽  
Archimedean Copulas

MODELING DEPENDENCE BETWEEN LOSS TRIANGLES WITH HIERARCHICAL ARCHIMEDEAN COPULAS

2015 ◽  
Vol 45 (3) ◽  
pp. 577-599 ◽  
Author(s):  
Anas Abdallah ◽  
Jean-Philippe Boucher ◽  
Hélène Cossette
Keyword(s):  
Life Insurance ◽  
Bootstrap Method ◽  
Dependence Structure ◽  
Insurance Company ◽  
Archimedean Copulas ◽  
Life Insurance Company ◽  
Critical Problems ◽  
Intuitive Interpretation ◽  
Property Casualty

AbstractOne of the most critical problems in property/casualty insurance is to determine an appropriate reserve for incurred but unpaid losses. These provisions generally comprise most of the liabilities of a non-life insurance company. The global provisions are often determined under an assumption of independence between the lines of business. Recently, Shi and Frees (2011) proposed to put dependence between lines of business with a copula that captures dependence between two cells of two different runoff triangles. In this paper, we propose to generalize this model in two steps. First, by using an idea proposed by Barnett and Zehnwirth (1998), we will suppose a dependence between all the observations that belong to the same calendar year (CY) for each line of business. Thereafter, we will then suppose another dependence structure that links the CYs of different lines of business. This model is done by using hierarchical Archimedean copulas. We show that the model provides more flexibility than existing models, and offers a better, more realistic and more intuitive interpretation of the dependence between the lines of business. For illustration, the model is applied to a dataset from a major US property-casualty insurer, where a bootstrap method is proposed to estimate the distribution of the reserve.

scholarly journals Extremal behavior of Archimedean copulas

2011 ◽  
Vol 43 (1) ◽  
pp. 195-216 ◽  
Author(s):  
Martin Larsson ◽  
Johanna Nešlehová
Keyword(s):  
Domain Of Attraction ◽  
Tail Dependence ◽  
Dependence Structure ◽  
Tail Behavior ◽  
Archimedean Copulas ◽  
Radial Part ◽  
Stochastic Representation ◽  
Lower Tail ◽  
Extremal Behavior ◽  
Practical Implications

We show how the extremal behavior of d-variate Archimedean copulas can be deduced from their stochastic representation as the survival dependence structure of an ℓ1-symmetric distribution (see McNeil and Nešlehová (2009)). We show that the extremal behavior of the radial part of the representation is determined by its Williamson d-transform. This leads in turn to simple proofs and extensions of recent results characterizing the domain of attraction of Archimedean copulas, their upper and lower tail-dependence indices, as well as their associated threshold copulas. We outline some of the practical implications of their results for the construction of Archimedean models with specific tail behavior and give counterexamples of Archimedean copulas whose coefficient of lower tail dependence does not exist.

scholarly journals Description of the Dependence Strength of Two Variogram Models of a Spatial Structure Using Archimedean Copulas

2017 ◽  
Vol 9 (1) ◽  
pp. 117
Author(s):  
Moumouni Diallo ◽  
Diakarya Barro
Keyword(s):  
Spatial Structure ◽  
Dependence Structure ◽  
Archimedean Copulas ◽  
Variogram Models ◽  
Measure Of Similarity

Variogram is a geostatistical tool which describes how the spatialcontinuity changes with a given separating distance between pairs of stations. In this paper, we study the dependence structure within a same class of bivariate spatialized archimedean copulas. Specifically, we point out properties of the gaussian variogram and the exponential one. A new measure of similarity of two copulas is computed particularly between the spatial independent copula and full dependence one.

scholarly journals Convergence of Archimedean copulas

2008 ◽  
Vol 78 (4) ◽  
pp. 412-419 ◽  
Author(s):  
Arthur Charpentier ◽  
Johan Segers
Keyword(s):  
Archimedean Copulas
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