The Tail Mean-Variance optimal capital allocation under the extended skew-elliptical distribution

In this paper we introduce a novel Tail Mean -Variance (TMV) model intended to optimize capital allocation in financial decision -making. The TMV model has many intriguing properties, such as considering the variability and tail risk of the loss function simultaneously. We specifically consider the multivariate extended skew -elliptical (ESE) distributions, which are widely applicable in financial and insurance data modeling. Additionally, we explore the probabilistic properties of the multivariate extended skew -elliptical (ESE) distributions and present explicit formulas for the TMV model within this distribution. Finally, a numerical example is provided to illustrate the results.