Publication: Multivariate extremality measure
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2010-06
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Abstract
We propose a new multivariate order based on a concept that we will call
extremality". Given a unit vector, the extremality allows to measure the
"farness" of a point with respect to a data cloud or to a distribution in the
vector direction. We establish the most relevant properties of this measure
and provide the theoretical basis for its nonparametric estimation. We
include two applications in Finance: a multivariate Value at Risk (VaR)
with level sets constructed through extremality and a portfolio selection
strategy based on the order induced by extremality.
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Extremality, Oriented cone, Value at risk, Portfolio selection