Multivariate Copulae

Though dating back to 1959 when the term “copulae” was coined, copula models only started their triumphal procession in the mid-1990s. Application of copulae was primarily restricted to the world of finance and insurance but now the copula concept has found its way into nearly all relevant statistical and mathematical literature where multivariate dependence structures are involved. Whereas the bivariate case was central in most of the publications and seems to be well-explored at present, there is still an ongoing and active debate on the construction of multivariate copula models. Apart from pair-copula constructions, which are the focus of this book and intensively discussed in the following chapters, this chapter briefly reviews both different copula classes and construction schemes of multivariate models.