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Risk measures like Marginal Expected Shortfall and Marginal Mean Excessquantify conditional risk and in particular, aid in the understanding ofsystemic risk. In many such scenarios, models exhibiting heavy tails in themargins and asymptotic tail independence in the joint behavior play afundamental role. The notion of hidden regular variation has the advantage thatit models both properties: asymptotic tail independence as well as heavy tails.An alternative approach to addressing these features is via copulas. First, weelicit connections between hidden regular variation and the behavior of tailcopula parameters extending previous works in this area. Then we study theasymptotic behavior of the aforementioned conditional excess risk measures;first under hidden regular variation and then under restrictions on the tailcopula parameters, not necessarily assuming hidden regular variation. Weprovide a broad variety of examples of models admitting heavy tails andasymptotic tail independence along with hidden regular variation and with theappropriate limit behavior for the risk measures of interest.

Hidden regular variation, copula models, and the limit behavior of conditional excess risk measures