TY - JOUR
T1 - Multivariate tail moments for log-elliptical dependence structures as measures of risks
AU - Landsman, Zinoviy
AU - Shushi, Tomer
N1 - Funding Information:
Funding: This research was supported by the Israel Science Foundation (Grant No. 1686/17).
Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.
PY - 2021/4/1
Y1 - 2021/4/1
N2 - 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.
AB - 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.
KW - Log-elliptical distributions
KW - Log-skew-elliptical distributions
KW - Multivariate tail conditional expectation
KW - Multivariate tail covariance
KW - Tail conditional expectation
UR - http://www.scopus.com/inward/record.url?scp=85103838690&partnerID=8YFLogxK
U2 - 10.3390/sym13040559
DO - 10.3390/sym13040559
M3 - Article
AN - SCOPUS:85103838690
VL - 13
JO - Symmetry
JF - Symmetry
SN - 2073-8994
IS - 4
M1 - 559
ER -