Genest et al. (1995) proposed a two-stages semi-parametric estimation procedure for bivariate Archimedean copulas. A three stage semi-parametric estimation method based on Kendall’s tau has been recently proposed in the financial literature to estimate the Student’s T copula, too. Its major advantage is to allow for greater computational tractability when dealing with high dimensional issues, w...

We choose two identically distributed dependent risks X1 and X2 with dependence structure modelled by an Archimedean copula. Then we are able to analyze diversification effects in the tails of aggregate dependent risks, i.e. for large u we study P [X1 +X2 ≥ u] ∼ c ·P [X1 ≥ u/2], where c describes the diversification effect.

We study continuous, nonnegative random variables with a Schur-constant joint survival function. We show that these distributions are characterized by having an Archimedean survival copula, determine the distributions of certain functions of the random variables, and examine dependence properties and correlation coefficients for random variables with Schur-constant survival functions.

We choose two identically distributed dependent risks X1 and X2 with dependence structure modelled by an Archimedean copula. Then we are able to analyze diversi...cation e¤ects in the tails of aggregate dependent risks, i.e. for large u we study P [X1+X2 ̧ u] » c ¢P [X1 ̧ u=2], where c describes the diversi...cation e¤ect.

In this paper, we introduce a new kind of order, Cesaro supermodular order, which includes supermodular order and stochastic order. For this new order, we show that it almost fulfils all desirable properties of a multivariate positive dependence order that have been proposed by Joe (1997). Also, we obtain some relations between it with other orders. Finally, we consider different issues related...

This paper presents a general tail approximation method for evaluating the Valueat-Risk of any norm of random vectors with multivariate regularly varying distributions. The main result is derived using the relation between the intensity measure of multivariate regular variation and tail dependence function of the underlying copula, and in particular extends the tail approximation discussed in E...

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 c...

Existing works on multivariate distributions mainly focus on limited distribution functions and require that the associated marginal distributions belong to the same family. Although this simplifies problems, it may fail to deal with practical cases when the marginal distributions are arbitrary. To this end, copula function is employed since it provides a flexible way in decoupling the marginal...