With the wider applicability of copula models in finance, insurance, hydrology, and biostatistics, new methodological challenges have emerged. This workshop will focus on four of them.

1- Multivariate copula models

There is a lack of flexible dependence structures for problems involving a large number of variables. Multivariate Archimedean and meta-elliptical copulas, which are often used in this context, are rather limited in this regard. Vine-copula constructions represent one highly promising alternative. This approach, which parallels classical hierarchical modeling, decomposes a multivariate distribution through a series of conditionings whose basic building blocks involve only pairs of variables. The systematic way in which this is done, called a vine, ensures that any choice of bivariate copula for the building blocks yields a bona fide multivariate distribution; compatibility issues are bypassed completely. Various estimation techniques for these models have recently been proposed, but much remains to be done to understand their finite-sample properties and asymptotic behavior. In addition, effective strategies for model selection are still lacking. The first objective of this workshop is to foster discussion among vine-copula specialists and identify possible solutions to these problems.

2- Dynamic copula models

Multivariate time series data are common in econometrics and finance. To capture serial as well as between-series dependence in such data, time series models are often fitted to the univariate series and copulas are used to account for the dependence between their innovations. Because the latter are unobservable, residuals are used as pseudo-observations to fit the copula, yielding methodological challenges that remain largely unexplored. The second objective of this workshop is to assess the merits of dynamic copula modeling and to explore estimation and goodness-of-fit procedures for such models.

3- Copulas and extremes

The study of extreme-value behaviour is crucial in many fields, e.g., hydrology and finance. Often, multivariate distributions exhibit dependence in the tails, despite the fact that the marginal distributions are not of an extreme-value type. In such circumstances, the estimation of the underlying extreme-value copula is of interest. There is currently a surge of activity around this theme: Bayesian and rank-based estimators of the Pickands dependence function have recently been proposed. Tests of extremeness and goodness-of-fit procedures have also been developed. However, diagnostic and prediction tools are still needed. In addition, most of the work in this area has been limited to the bivariate case. The third objective of the workshop is to bring together experts in copulas, extreme-value theory, hydrology, and finance to stimulate the ongoing activities in this research.

4- Copulas with incomplete data

Biostatistics is a prime area of application for copula models, as the traditional assumption of multivariate normality is usually invalid in this context. Typically, data collection mechanisms in biostatistics involve censoring, truncation, or other types of incomplete observations. Moreover, response variables are often discrete and explanatory variables must be taken into account. These data characteristics create many challenges for copula inference, which was originally developed for continuous observations. Problems include the lack of uniqueness of the copula, the presence of ties in the ranks, and numerical problems in the evaluation of probabilities of events in high dimension. The last objective of the workshop is to foster collaboration among the main contributors to this emerging area of research.