  In univariate data, there exist standard procedures for identifying
dominating features that produce the largest observations. However, in the
multivariate setting, the situation is quite different. This paper aims to
provide tools and algorithms for detecting dominating directional components in
multivariate data.
  We study general heavy-tailed multivariate random vectors in dimension $d\geq
2$ and present consistent estimators which can be used to evaluate why the data
is heavy-tailed. This is done by identifying the set of the riskiest
directional components. The results are of particular interest in insurance
when setting reinsurance policies and in finance when hedging a portfolio of
multiple assets.
