We present general results on the univariate tail conditional expectation (TCE) and multivariate tail conditional expectation (MTCE) for location-scale mixture of elliptical distributions. Examples include the location-scale mixture of normal distributions, location-scale mixture of Student-$t$ distributions, location-scale mixture of logistic distributions and location-scale mixture of Laplace distributions. We also consider portfolio risk decomposition with TCE for location-scale mixture of elliptical distributions. More specifically, we give MTCEs of generalized hyperbolic and slash distributions, and discuss the difference of MTCEs for generalized hyperbolic and slash distributions. As an illustrative example, we discuss the MTCE of five stocks including Amazon, Goldman Sachs, IBM, Google and Apple.

我们展示了椭圆分布的位置尺度混合的单变量尾部条件期望（TCE）和多变量尾部条件期望（MTCE）的一般结果。示例包括正态分布的位置尺度混合、学生-$吨$分布、逻辑分布的位置尺度混合和拉普拉斯分布的位置尺度混合。我们还考虑使用 TCE 对椭圆分布的位置尺度混合进行投资组合风险分解。更具体地说，我们给出了广义双曲线和斜线分布的 MTCE，并讨论了广义双曲线和斜线分布的 MTCE 的差异。作为说明性示例，我们讨论了亚马逊、高盛、IBM、谷歌和苹果等五只股票的 MTCE。