Multivariate extremality measure
AbstractWe 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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Bibliographic InfoPaper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws101908.
Date of creation: Jun 2010
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Extremality; Oriented cone; Value at risk; Portfolio selection;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-07-03 (All new papers)
- NEP-ECM-2010-07-03 (Econometrics)
- NEP-MIC-2010-07-03 (Microeconomics)
- NEP-RMG-2010-07-03 (Risk Management)
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