Being the limits of copulas of componentwise maxima in independent random samples, extreme-value copulas can be considered to provide appropriate models for the dependence structure between rare events. Extreme-value copulas not only arise naturally in the domain of extreme-value theory, they can also be a convenient choice to model general positive dependence structures. The aim of this survey is to present the reader with the state-of-the-art in dependence modeling via extreme-value copulas. Both probabilistic and statistical issues are reviewed, in a nonparametric as well as a parametric context.
Gudendorf, G., & Segers, J. (2010). Extreme-value copulas. In Piotr Jaworski, Fabrizio Durante, Wolfgang Karl Härdle, Tomasz Richlik (ed.), Copula theory and its applications (p. p. 127-145). Springer. https://doi.org/10.1007/978-3-642-12465-5_6