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A new notion of stochastic ordering is introduced to compare multivariatestochastic risk models with respect to extreme portfolio losses. In theframework of multivariate regular variation comparison criteria are derived interms of ordering conditions on the spectral measures, which allows foranalytical or numerical verification in practical applications. Additionalcomparison criteria in terms of further stochastic orderings are derived. Theapplication examples include worst case and best case scenarios, ellipticallycontoured distributions, and multivariate regularly varying models with Gumbel,Archimedean, and Galambos copulas.

Ordering of multivariate probability distributions with respect to extreme portfolio losses