The tail behavior of sums of dependent risks was considered by Wüthrich (2003) and by Alink et al. (2004, 2005) in the case where the variables are exchangeable and connected through an Archimedean copula model. It is shown here how their result can be extended to a broader class of dependence structures using multivariate extreme-value theory. An explicit form is given for the asymptotic proba...

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...

The Copula approach can be used to describe the dependence structure between variables. In this paper, by using a Bivariate Clayton copula, we discuss statistical analysis of simple step-stress accelerated dependent competing failure model under progressively Type-II censoring sample. With assumption cumulative exposure, Bayesian estimations parameters are derived. Based on Monte-Carlo simulati...

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 introduce a statistical test for comparing the predictive accuracy of competing copula specifications in multivariate density forecasts, based on the Kullback-Leibler Information Criterion (KLIC). The test is valid under general conditions on the competing copulas: in particular it allows for parameter estimation uncertainty and for the copulas to be nested or non-nested. Monte Carlo simulat...

Copulae is a growing field of interest and application for dependency modelling. There is however no predominant way of choosing the copula model that best fits a given data set. We introduce a new goodness-of-fit test, based on the probability integral transform. The test is consistent, numerically efficient and incorporates a weighting functionality. Results show that the test performs well a...

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.