In the insurance and financial markets, events of extreme losses happen in the tail of return distributions, and investors are sensitive to these losses. The Tail Mean–Variance (TMV) criterion focuses on the rare risk but large losses, and it has recently been used in financial management for portfolio selection. In this paper, the proposed TMV criterion is based on the two measures of risk, i.e., the Tail Conditional Expectation (TCE) and Tail Variance (TV) under Generalized Skew-Elliptical (GSE) distribution. We obtain an explicit solution with simple implementation and use a convex optimization approach for the TMV optimization problem under the GSE distribution. We also provide a practical example of a portfolio optimization problem using the proposed TMV criterion. The empirical results show that the optimal portfolio performance can be improved by controlling the tail variability of returns distribution.

在保险和金融市场中，极端损失的事件发生在收益分配的尾部，投资者对这些损失非常敏感。尾部均值-方差（TMV）准则侧重于稀有风险但损失巨大，最近已在财务管理中用于选择投资组合。在本文中，提出的TMV标准基于两种风险度量，即广义斜椭圆（GSE）分布下的尾部条件期望（TCE）和尾部方差（TV）。我们获得了具有简单实现的显式解决方案，并针对GSE分布下的TMV优化问题使用了凸优化方法。我们还提供了使用建议的TMV准则进行投资组合优化问题的实际示例。