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Multivariate extremality measure

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URI: https://hdl.handle.net/10016/8970
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ws101908.pdf (6.17 MB)
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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
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DES - Working Papers. Statistics and Econometrics. WS