Tasche [Tasche, D., 1999. Risk contributions and performance measurement. Working paper, Technische Universitat Munchen] introduces a capital allocation principle where the capital allocated to each risk unit can be expressed in terms of its contribution to the conditional tail expectation (CTE) of the aggregate risk. Panjer [Panjer, H.H., 2002. Measurement of risk, solvency requirements and allocation of capital within financial conglomerates. Institute of Insurance and Pension Research, University of Waterloo, Research Report 01-15] derives a closed-form expression for this allocation rule in the multivariate normal case. Landsman and Valdez [Landsman, Z., Valdez, E., 2002. Tail conditional expectations for elliptical distributions. North American Actuarial J. 7 (4)] generalize Panjer's result to the class of multivariate elliptical distributions. In this paper we provide an alternative and simpler proof for the CTE-based allocation formula in the elliptical case. Furthermore, we derive accurate and easy computable closed-form approximations for this allocation formula for sums that involve normal and lognormal risks.
Tasche, D.， 1999。风险贡献和绩效度量。工作论文，慕尼黑工业大学]介绍了一种资本分配原则，其中分配给每个风险单位的资本可以根据其对总风险的条件尾部期望(CTE)的贡献来表示。潘杰[H.H.]， 2002。金融集团内部的风险度量、偿付能力要求和资本配置。滑铁卢大学保险与养老金研究所，研究报告01-15]推导了多元正态情况下该分配规则的封闭表达式。Â兰德斯曼和瓦尔迪兹[兰德斯曼，Z.，瓦尔迪兹，E.， 2002.]椭圆分布的尾部条件期望。North American Actuarial J. 7(4)]将Panjer的结果推广到一类多变量椭圆分布。本文给出了椭圆情况下基于cte的分配公式的另一种更简单的证明。此外，对于涉及正态和对数正态风险的总和，我们导出了该分配公式的精确且易于计算的封闭近似。
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