CAPITAL ALLOCATION WITH MULTIVARIATE RISK MEASURES: AN AXIOMATIC APPROACH
CAPITAL ALLOCATION WITH MULTIVARIATE RISK MEASURES: AN AXIOMATIC APPROACH
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DOI：
10.1017/s0269964819000032
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发表时间：
2020-04
影响因子：
1.1
通讯作者：
Linxiao Wei;Yijun Hu
中科院分区：
文献类型：
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作者：
Linxiao Wei;Yijun Hu
摘要资本配置在投资组合管理和基于风险的业绩衡量中至关重要。单变量风险度量的资本分配在金融文献中得到了广泛的研究。与这种情况形成对比的是，很少有论文讨论多元风险衡量的资本分配问题。在本文中，我们提出了一个多元风险度量的资本配置公理体系。我们首先回顾了一类正齐次可加的多元风险度量，并给出了相应的表示结果。证明了对于给定的正齐次可加多元风险度量，存在资本分配原理。此外，还对资本分配原则的唯一性进行了刻画。最后，给出了基于均值和标准差的多元风险度量(包括多元均值-标准差风险度量)的显式资本配置原则。
Abstract Capital allocation is of central importance in portfolio management and risk-based performance measurement. Capital allocations for univariate risk measures have been extensively studied in the finance literature. In contrast to this situation, few papers dealt with capital allocations for multivariate risk measures. In this paper, we propose an axiom system for capital allocation with multivariate risk measures. We first recall the class of the positively homogeneous and subadditive multivariate risk measures, and provide the corresponding representation results. Then it is shown that for a given positively homogeneous and subadditive multivariate risk measure, there exists a capital allocation principle. Furthermore, the uniqueness of the capital allocation principe is characterized. Finally, examples are also given to derive the explicit capital allocation principles for the multivariate risk measures based on mean and standard deviation, including the multivariate mean-standard-deviation risk measures.