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Vector-Valued Multivariate Conditional Value-at-Risk

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  • Merve Merakli
  • Simge Kucukyavuz

Abstract

In this study, we propose a new definition of multivariate conditional value-at-risk (MCVaR) as a set of vectors for discrete probability spaces. We explore the properties of the vector-valued MCVaR (VMCVaR) and show the advantages of VMCVaR over the existing definitions given for continuous random variables when adapted to the discrete case.

Suggested Citation

  • Merve Merakli & Simge Kucukyavuz, 2017. "Vector-Valued Multivariate Conditional Value-at-Risk," Papers 1708.01324, arXiv.org.
    • Handle: RePEc:arx:papers:1708.01324
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    References listed on IDEAS

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    1. Torres Díaz, Raúl Andrés & Lillo Rodríguez, Rosa Elvira & Laniado Rodas, Henry, 2015. "A Directional Multivariate Value at Risk," DES - Working Papers. Statistics and Econometrics. WS ws1501, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Nilay Noyan & Gábor Rudolf, 2013. "Optimization with Multivariate Conditional Value-at-Risk Constraints," Operations Research, INFORMS, vol. 61(4), pages 990-1013, August.
    3. 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.
    4. Di Bernardino, E. & Fernández-Ponce, J.M. & Palacios-Rodríguez, F. & Rodríguez-Griñolo, M.R., 2015. "On multivariate extensions of the conditional Value-at-Risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 1-16.
    5. Cousin, Areski & Di Bernardino, Elena, 2014. "On multivariate extensions of Conditional-Tail-Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 272-282.
    6. Areski Cousin & Elena Di Bernadino, 2013. "On Multivariate Extensions of Value-at-Risk," Working Papers hal-00638382, HAL.
    7. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    8. Areski Cousin & Elena Di Bernadino, 2011. "On Multivariate Extensions of Value-at-Risk," Papers 1111.1349, arXiv.org, revised Apr 2013.
    9. Cousin, Areski & Di Bernardino, Elena, 2013. "On multivariate extensions of Value-at-Risk," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 32-46.
    10. Jinwook Lee & András Prékopa, 2013. "Properties and calculation of multivariate risk measures: MVaR and MCVaR," Annals of Operations Research, Springer, vol. 211(1), pages 225-254, December.
    11. Ra'ul Torres & Rosa E. Lillo & Henry Laniado, 2015. "A Directional Multivariate Value at Risk," Papers 1502.00908, arXiv.org.
    12. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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