Multivariate tail moments for log-elliptical dependence structures as measures of risks

Zinoviy Landsman, Tomer Shushi

Research output: Contribution to journalArticlepeer-review


The class of log-elliptical distributions is well used and studied in risk measurement and actuarial science. The reason is that risks are often skewed and positive when they describe pure risks, i.e., risks in which there is no possibility of profit. In practice, risk managers confront a system of mutually dependent risks, not only one risk. Thus, it is important to measure risks while capturing their dependence structure. In this short paper, we compute the multivariate risk measures, multivariate tail conditional expectation, and multivariate tail covariance measure for the family of log-elliptical distributions, which captures the dependence structure of the risks while focusing on the tail of their distributions, i.e., on extreme loss events. We then study our result and examine special cases, as well as the optimal portfolio selection using such measures. Finally, we show how the given multivariate tail moments can also be computed for log-skew elliptical models based on similar approaches given for the log-elliptical case.

Original languageEnglish
Article number559
Issue number4
StatePublished - Apr 2021

Bibliographical note

Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.


  • Log-elliptical distributions
  • Log-skew-elliptical distributions
  • Multivariate tail conditional expectation
  • Multivariate tail covariance
  • Tail conditional expectation

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • General Mathematics
  • Physics and Astronomy (miscellaneous)


Dive into the research topics of 'Multivariate tail moments for log-elliptical dependence structures as measures of risks'. Together they form a unique fingerprint.

Cite this