MULTIVARIATE RISK MEASURES: A CONSTRUCTIVE APPROACH BASED ON SELECTIONS
MULTIVARIATE RISK MEASURES: A CONSTRUCTIVE APPROACH BASED ON SELECTIONS
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DOI：
10.1111/mafi.12078
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发表时间：
2013-01
影响因子：
1.6
通讯作者：
I. Molchanov;I. Cascos
中科院分区：
文献类型：
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作者：
I. Molchanov;I. Cascos
由于多元投资组合中的风险头寸可以通过取决于交换规则和相关交易成本的资本要求的各种选择来抵消，因此很自然地假设随机向量的风险度量是设定值的。此外，将交换规则包含在风险度量的参数中是合理的，因此考虑设定值投资组合的风险度量。这种情况包括经典的卡巴诺夫交易成本模型，其中设定值投资组合由随机向量和交换锥之和给出，而且还包括许多额外流动性约束的进一步情况。我们建议风险度量的定义基于如果设定值投资组合具有所有单独可接受的边际的选择，则该投资组合是可接受的。获得的选择风险度量是相干的（或凸的）、规律不变的，并且具有上凸闭集的值。我们描述了选择风险度量的双重表示，并提出了从下到上近似它的有效方法。在卡巴诺夫交换锥模型中，显示了选择风险测度与 Kulikov (2008, Theory Probab. Appl. 52, 614–635)、Hamel 和 Heyde (2010, SIAM J. Financ. Math. 1, 66–95) 以及 Hamel、Heyde 和 Rudloff (2013, Math. 10) 考虑的集值风险测度之间的关系。金融。 5、 1-28）。
Since risky positions in multivariate portfolios can be offset by various choices of capital requirements that depend on the exchange rules and related transaction costs, it is natural to assume that the risk measures of random vectors are set‐valued. Furthermore, it is reasonable to include the exchange rules in the argument of the risk measure and so consider risk measures of set‐valued portfolios. This situation includes the classical Kabanov's transaction costs model, where the set‐valued portfolio is given by the sum of a random vector and an exchange cone, but also a number of further cases of additional liquidity constraints. We suggest a definition of the risk measure based on calling a set‐valued portfolio acceptable if it possesses a selection with all individually acceptable marginals. The obtained selection risk measure is coherent (or convex), law invariant, and has values being upper convex closed sets. We describe the dual representation of the selection risk measure and suggest efficient ways of approximating it from below and from above. In the case of Kabanov's exchange cone model, it is shown how the selection risk measure relates to the set‐valued risk measures considered by Kulikov (2008, Theory Probab. Appl. 52, 614–635), Hamel and Heyde (2010, SIAM J. Financ. Math. 1, 66–95), and Hamel, Heyde, and Rudloff (2013, Math. Financ. Econ. 5, 1–28).