Asymptotics for risk capital allocations based on Conditional Tail Expectation

An investigation of the limiting behavior of a risk capital allocation rule based on the Conditional Tail Expectation (CTE) risk measure is carried out. More specifically, with the help of general notions of Extreme Value Theory (EVT), the aforementioned risk capital allocation is shown to be asymptotically proportional to the corresponding Value-at-Risk (VaR) risk measure. The existing methodology acquired for VaR can therefore be applied to a somewhat less well-studied CTE. In the context of interest, the EVT approach is seemingly well-motivated by modern regulations, which openly strive for the excessive prudence in determining risk capitals.

► We study capital allocations based on the Conditional Tail Expectation risk measure. ► We propose to tackle the problem at high confidence levels. ► Extreme value theory and vague convergence are employed. ► Both asymptotic dependence and asymptotic independence are considered. ► Capital allocations are shown to be asymptotically proportional to the corresponding Value-at-Risk risk measure.