Complete mixability and asymptotic equivalence of worst-possible VaR and ES estimates

We give a new sufficient condition for a continuous distribution to be completely mixable, and we use this condition to show that the worst-possible value-at-risk for the sum of d inhomogeneous risks is equivalent to the worst-possible expected shortfall under the same marginal assumptions, in the limit as d→∞. Numerical applications show that this equivalence holds also for relatively small dimensions d.