The modeling of joint probability distributions of correlated variables and the evaluation of reliability under incomplete probability information remain a challenge that has not been studied extensively. This article aims to investigate the effect of copulas for modeling dependence structures between variables on reliability under incomplete probability information. First, a copula-based metho...

This report summarizes my contributions to copulas modeling. Two main research topics are addressed: The construction of semiparametric family of copulas based on a set of orthonormal functions and a matrix and the design of efficient estimation procedures.

The extremal dependence of a random vector describes the tail behaviors of joint probabilities of the random vector with respect to that of its margins, and has been often studied by using the tail dependence function of its copula. A tail density approach is introduced in this paper to analyze extremal dependence of the copulas that are specified only by densities. The relation between the cop...

This paper proposes a new approach to measure dependences in multivariate financial data. Data in finance and insurance often cover a long time period. Therefore, the economic factors may induce some changes inside the dependence structure. Recently, two methods using copulas have been proposed to analyze such changes. The first approach investigates changes inside copula’s parameters. The seco...

This paper presents algorithms for generating random variables for exponential/Rayleigh/ Weibull, Nakagami-m and Rician copulas with any desired copula parameter(s), using the direct conditional cumulative distribution function method and the complex Gaussian distribution method. Moreover, a novel method for optimal copula selection is also proposed, based on the criterion that for a given seri...

The Pairwise Markov Chain (PMC) model assumes the couple of observations and states processes to be aMarkov chain. To extend themodeling capability of class-conditional densities involved in the PMC model, copulas are introduced and the influence of their shape on classification error rates is studied. In particular, systematic experiments show that the use of wrong copulas can degrade signific...

Copulas allow to learn marginal distributions separately from the multivariate dependence structure (copula) that links them together into a density function. Vine factorizations ease the learning of high-dimensional copulas by constructing a hierarchy of conditional bivariate copulas. However, to simplify inference, it is common to assume that each of these conditional bivariate copulas is ind...

This paper proposes a new approach to measure dependences in multivariate financial data. Data in finance and insurance often cover a long time period. Therefore, the economic factors may induce some changes inside the dependence structure. Recently, two methods using copulas have been proposed to analyze such changes. The first approach investigates changes inside copula’s parameters. The seco...

The aim of this paper is to use copulas functions to capture the different structures of dependency when we deal with portfolios of dependent credit risks and a basket of credit derivatives. We first present the wellknown result for the pricing of default risk, when there is only one defaultable firm. After that, we expose the structure of dependency with copulas in pricing dependent credit der...