From Inequality to Extremes and Back: A Lorenz Representation of the Pickands Dependence Function

We establish a correspondence between Lorenz curves and Pickands dependence functions, thereby reframing the construction of any bivariate extreme‑value copula as an inequality problem. We discuss the conditions under which a Lorenz curve generates a closed‑form Pickands model, considerably expanding the small set of tractable parametrizations currently available. Furthermore, the Pickands measure‑generating function M can be written explicitly in terms of the quantile function underlying the Lorenz curve, providing a constructive route to model specification. Finally, classical inequality indices like the Gini coincide with scale‑free, rotation‑invariant indices of global upper‑tail dependence, thereby complementing local coefficients such as the upper tail dependence index λ U .