Tail Variance premiums for log-elliptical distributions

In this paper we derive expressions for the Tail Variance and the Tail Variance Premium of risks in a multivariate log-elliptical setting. The theoretical results are illustrated by considering lognormal and log-Laplace distributions. We also derive approximate expressions for a Tail Variance-based allocation rule in a multivariate lognormal setting. A numerical example illustrates the accurateness of the proposed approximations.