Tail comonotonicity: Properties, constructions, and asymptotic additivity of risk measures

We investigate properties of a version of tail comonotonicity that can be applied to absolutely continuous distributions, and give several methods for constructions of multivariate distributions with tail comonotonicity or strongest tail dependence. Archimedean copulas as mixtures of powers, and scale mixtures of a non-negative random vector with the mixing distribution having slowly varying tails, lead to a tail comonotonic dependence structure. For random variables that are in the maximum domain of attraction of either Fréchet or Gumbel, we prove the asymptotic additivity property of Value at Risk and Conditional Tail Expectation.