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Deheuvels (1981a) described a decomposition of the empirical copula process into a finite number of asymptotically mutually independent sub-processes whose joint limiting distribution is tractable under the hypothesis that a multivariate distribution is equal to the product of its margins. It is proved here that this result can be extended to the serial(More)
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(More)
There is a growing concern in the actuarial literature for the effect of dependence between individual risks X i on the distribution of the aggregate claim S = X 1 + · · · + X n. has led, among other things, to the identification of the portfolio yielding the smallest and largest stop-loss premiums and hence to bounds on E{φ(S)} for arbitrary(More)
This paper presents an introduction to inference for copula models, based on rank methods. By working out in detail a small, fictitious numerical example, the writers exhibit the various steps involved in investigating the dependence between two random variables and in modeling it using copulas. Simple graphical tools and numerical techniques are presented(More)
When a decision maker chooses to form his/her own probability distribution by combining the opinions of a number of experts, it is sometimes recommended that he/she should do so in such a way as to preserve any form of expert agreement regarding the independence of the events of interest. In this paper, we argue against this recommendation. We show that for(More)
Any multivariate density can be decomposed through successive condition-ings into basic building blocks involving only pairs of variables. The various ways in which this can be done are called regular vines; C-vines and D-vines are prime examples of such structures. A pair-copula construction (PCC) is a modelling strategy in which conditional and(More)
Oakes (1994) described in broad terms an omnibus semiparametric procedure for estimating the dependence parameter in a copula model when marginal distributions are treated as (infinite-dimensional) nuisance parameters. The resulting estimator was subsequently shown to be consistent and normally distributed asymp-totically (Genest et al. 1995, Shih and Louis(More)