COPULAS EVERYWHERE

Copulas Everywhere: Statistics, Analysis, Probability, and Evolution, is a self-contained graduate-level treatment of copula theory, separating a joint distribution's dependence structure from its marginal behaviour.

Starting from Sklar's theorem, the book develops the subject along three strands: statistics (rank correlations, tail dependence, risk models), functional analysis (the space of copulas as a compact, convex object), and probability (copulas generated by stochastic processes). A preliminaries chapter reviews Gaussian vectors and Markov operators before the main construction methods: inversion, perturbation, and Archimedean generators.

A running theme, and the author's own contribution, is symmetry and asymmetry: how far a copula departs from exchangeability, and how to build new asymmetric families. Later chapters cover compatibility of low-dimensional copulas, elliptical and holomorphic regularizations, and evolution copulas that change in time. A closing chapter applies the theory to insurance and finance, including the Gaussian copula's role in the 2008 crisis. Three appendices offer exercises, alternative proofs of Sklar's theorem, and a prototype exam.