Arthur Charpentier

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A complete and user-friendly directory of tails of Archimedean copulas is presented which can be used in the selection and construction of appropriate models with desired properties. The results are synthesized in the form of a decision tree: Given the values of some readily computable characteristics of the Archimedean generator, the upper and lower tails(More)
Dependence structures for bivariate extremal events are analyzed using particular types of copula. Weak convergence results for copulas along the lines of the Pickands–Balkema– de Haan theorem provide limiting dependence structures for bivariate tail events. A characterization of these limiting copulas is also provided by means of invariance properties. The(More)
Copula modelling has become ubiquitous in modern statistics. Here, the problem of nonparametrically estimating a copula density is addressed. Arguably the most popular nonparametric density estimator, the kernel estimator is not suitable for the unit-square-supported copula densities, mainly because it is heavily a↵ected by boundary bias issues. In(More)
INTRODUCTION Copulas are a way of formalising dependence structures of random vectors. Although they have been known about for a long time (Sklar (1959)), they have been rediscovered relatively recently in applied sciences (biostatistics, reliability, biology, etc). In finance, they have become a standard tool with broad applications: multiasset pricing(More)
In this paper we suggest several nonparametric quantile estimators based on Beta kernel. They are applied to transformed data by the generalized Champernowne distribution initially fitted to the data. A Monte Carlo based study has shown that those estimators improve the efficiency of the traditional ones, not only for light tailed distributions, but also(More)
The IPCC 2007 report noted that both the frequency and strength of hurricanes, floods and droughts have increased during the past few years. Thus, climate risk, and more specifically natural catastrophes, are now hardly insurable: losses can be huge (and the actuarial pure premium might even be infinite), diversification through the central limit theorem is(More)
Convergence of a sequence of bivariate Archimedean copulas to another Archimedean copula or to the comonotone copula is shown to be equivalent with convergence of the corresponding sequence of Kendall distribution functions. No extra differentiability conditions on the generators are needed. r 2007 Elsevier B.V. All rights reserved.
Value-at-Risk, despite being adopted as the standard risk measure in finance, suffers severe objections from a practical point of view, due to a lack of convexity, and since it does not reward diversification (which is an essential feature in portfolio optimization). Furthermore, it is also known as having poor behavior in risk estimation (which has been(More)
This paper proposes a general framework to compare the strength of the dependence in survival models, as time changes, i. e. given remaining lifetimes X , to compare the dependence of X given X > t, and X given X > s, where s > t. More precisely, analytical results will be obtained in the case the survival copula of X is either Archimedean or a distorted(More)
The paper explores different applications of the Shapley value for either inequality or poverty measures. We first investigate the problem of source decomposition of inequality measures, the so-called additive income sources inequality games, baed on the Shapley Value, introduced by Chantreuil and Trannoy (1999) and Shorrocks (1999). We show that(More)