  Risk measures like Marginal Expected Shortfall and Marginal Mean Excess
quantify conditional risk and in particular, aid in the understanding of
systemic risk. In many such scenarios, models exhibiting heavy tails in the
margins and asymptotic tail independence in the joint behavior play a
fundamental role. The notion of hidden regular variation has the advantage that
it models both properties: asymptotic tail independence as well as heavy tails.
An alternative approach to addressing these features is via copulas. First, we
elicit connections between hidden regular variation and the behavior of tail
copula parameters extending previous works in this area. Then we study the
asymptotic behavior of the aforementioned conditional excess risk measures;
first under hidden regular variation and then under restrictions on the tail
copula parameters, not necessarily assuming hidden regular variation. We
provide a broad variety of examples of models admitting heavy tails and
asymptotic tail independence along with hidden regular variation and with the
appropriate limit behavior for the risk measures of interest.
