# subadditivity of VaR

It is known that the VaR (Value at risk) doesn't fulfill subadditivity, i.e.

$VaR(X)+VaR(Y) \le VaR(X+Y)$

But for elliptical distributions subadditivity is true. Questions:

(1) Which distributions are elliptical? I guess its the (multi)normal and t-distributions...Are stable and hyperbolic distributions elliptical,too?

(2) Is subadditvity only fulfilled for elliptical distributions? Are there any other conditions (e.g. correlation) which have an impact on subadditivity of VaR?

• The book "Quantitative Risk Management - Concepts, Techniques and Tools" may provide you an answer. – Gordon May 12 '16 at 15:08