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Multivariate extremality measure

Author

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  • Laniado Rodas, Henry
  • Romo Urroz, Juan
  • Lillo Rodríguez, Rosa Elvira

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.

Suggested Citation

  • Laniado Rodas, Henry & Romo Urroz, Juan & Lillo Rodríguez, Rosa Elvira, 2010. "Multivariate extremality measure," DES - Working Papers. Statistics and Econometrics. WS ws101908, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:ws101908
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    Cited by:

    1. Laniado Rodas, Henry & Lillo Rodríguez, Rosa Elvira & Torres Díaz, Raúl Andrés & Michele, Carlo de, 2016. "Directional multivariate extremes in environmental phenomena," DES - Working Papers. Statistics and Econometrics. WS 23419, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Torres, Raúl & Lillo, Rosa E. & Laniado, Henry, 2015. "A directional multivariate value at risk," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 111-123.

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    Keywords

    Extremality;

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