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Properties and calculation of multivariate risk measures: MVaR and MCVaR

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  • Jinwook Lee
  • András Prékopa

Abstract

A recent paper by Prékopa (Ann. Oper. Res. 193(1):49–69, 2012 ) presented results in connection with Multivariate Value-at-Risk (MVaR) that has been known for some time under the name of p-quantile or p-Level Efficient Point (pLEP) and introduced a new multivariate risk measure, called Multivariate Conditional Value-at-Risk (MCVaR). The purpose of this paper is to further develop the theory and methodology of MVaR and MCVaR. This includes new methods to numerically calculate MCVaR, for both continuous and discrete distributions. Numerical examples with recent financial market data are presented. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:211:y:2013:i:1:p:225-254:10.1007/s10479-013-1482-5
    DOI: 10.1007/s10479-013-1482-5
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    References listed on IDEAS

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    Cited by:

    1. Yuanyuan SUI & Adelina DUMITRESCU – PECULEA, 2016. "Financial risk identification and control of cross border merger and acquisition enterprises," The Audit Financiar journal, Chamber of Financial Auditors of Romania, vol. 14(144), pages 1368-1368.
    2. Andres Mauricio Molina Barreto & Naoyuki Ishimura, 2023. "Remarks on a copula‐based conditional value at risk for the portfolio problem," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 30(3), pages 150-170, July.
    3. Limin Wen & Junxue Li & Tong Pu & Yiying Zhang, 2024. "Comparisons of multivariate contribution measures of risk contagion and their applications in cryptocurrency market," Papers 2411.13384, arXiv.org.
    4. Qi Liu & Gengzhong Feng & Nengmin Wang & Giri Kumar Tayi, 2018. "A multi-objective model for discovering high-quality knowledge based on data quality and prior knowledge," Information Systems Frontiers, Springer, vol. 20(2), pages 401-416, April.
    5. Merve Merakli & Simge Kucukyavuz, 2017. "Vector-Valued Multivariate Conditional Value-at-Risk," Papers 1708.01324, arXiv.org.
    6. Aray Almen & Darinka Dentcheva, 2024. "On Risk Evaluation and Control of Distributed Multi-agent Systems," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 2025-2054, November.
    7. Jinwook Lee & András Prékopa, 2015. "Decision-making from a risk assessment perspective for Corporate Mergers and Acquisitions," Computational Management Science, Springer, vol. 12(2), pages 243-266, April.
    8. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2015. "Shortfall Deviation Risk: An alternative to risk measurement," Papers 1501.02007, arXiv.org, revised May 2016.
    9. Sordo, Miguel A., 2016. "A multivariate extension of the increasing convex order to compare risks," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 224-230.
    10. Prékopa, András & Lee, Jinwook, 2018. "Risk tomography," European Journal of Operational Research, Elsevier, vol. 265(1), pages 149-168.
    11. Cousin, Areski & Di Bernardino, Elena, 2014. "On multivariate extensions of Conditional-Tail-Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 272-282.
    12. 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.
    13. Qi Liu & Gengzhong Feng & Nengmin Wang & Giri Kumar Tayi, 0. "A multi-objective model for discovering high-quality knowledge based on data quality and prior knowledge," Information Systems Frontiers, Springer, vol. 0, pages 1-16.

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