  The concept of univariate Range Value-at-Risk, presented by Cont et al.
(2010), is extended in the multidimensional setting. Traditional risk measures
are not well suited when dealing with heavy-tail distributions and infinite
tail expectations. The multivariate definitions of robust truncated tail
expectations are provided to overcome this problem. Robustness and other
properties as well as empirical estimators are derived. Closed-form expressions
and special cases in the extreme value framework are also discussed. Numerical
and graphical examples are provided to examine the accuracy of the empirical
estimators.
