The multivariate regular variation (MRV) is one of the most important tools in modelling multivariate heavy-tailed phenomena. This paper characterizes the MRV distribution through the upper tail dependence index of the copula associated with them. Along with Theorem 2.3 in Li and Sun (2009), our...

Tail Mean-Variance (TMV) has emerged from the actuarial community as a criterion for risk management and portfolio selection, with a focus on extreme losses. The existing literature on portfolio optimization under the TMV criterion relies on the plug-in approach that substitutes the unknown mean...