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Multivariate range Value-at-Risk and covariance risk measures for elliptical and log-elliptical distributions

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  • Baishuai Zuo
  • Chuancun Yin
  • Jing Yao

Abstract

In this article, we propose the multivariate range Value-at-Risk (MRVaR) and the multivariate range covariance (MRCov) as two risk measures and explore their desirable properties in risk management. To facilitate analytical analyses, we derive explicit expressions of the MRVaR and the MRCov in the context of the multivariate (log-)elliptical distribution family. Frequently-used cases in industry, such as normal, student-t, logistic, Laplace, and Pearson type VII distributions, are presented with numerical examples. As an application, we propose a range-based mean-variance framework for optimal portfolio selection.

Suggested Citation

  • Baishuai Zuo & Chuancun Yin & Jing Yao, 2025. "Multivariate range Value-at-Risk and covariance risk measures for elliptical and log-elliptical distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 54(9), pages 2690-2722, May.
    • Handle: RePEc:taf:lstaxx:v:54:y:2025:i:9:p:2690-2722
    DOI: 10.1080/03610926.2024.2372472
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