Ordering of multivariate probability distributions with respect to extreme portfolio losses

Details Ordering of multivariate probability distributions with respect to extreme portfolio losses Ordering of multivariate probability distributions with respect to extreme portfolio losses

2010-10-25

arxiv.org/abs/1010.5171v1

Economy

Quantitative Finance

Risk Management

Scientific paper

A new notion of stochastic ordering is introduced to compare multivariate stochastic risk models with respect to extreme portfolio losses. In the framework of multivariate regular variation comparison criteria are derived in terms of ordering conditions on the spectral measures, which allows for analytical or numerical verification in practical applications. Additional comparison criteria in terms of further stochastic orderings are derived. The application examples include worst case and best case scenarios, elliptically contoured distributions, and multivariate regularly varying models with Gumbel, Archimedean, and Galambos copulas.

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