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摘要翻译：
由于多变量投资组合中的风险头寸可以通过取决于交易规则和相关交易费用的各种资本要求选择来抵消，因此很自然地假设随机向量的风险度量是集值的。此外，在风险测度的论证中加入交换规则，从而考虑集值投资组合的风险测度是合理的。这种情况包括经典的Kabanov交易费用模型，其中集值投资组合是由随机向量和交换锥之和给出的，但也包括许多额外流动性约束的进一步情况。我们提出了一个风险度量的定义，如果一个集值投资组合拥有一个具有所有独立可接受边际的选择，则将其称为可接受的。所得到的选择风险测度是相干的（或凸的）、律不变的，且其值为上凸闭集。我们描述了选择风险度量的对偶表示，并提出了从下面和从上面逼近它的有效方法。在Kabanov的交换锥模型中，给出了选择风险度量与Kulikov(2008)、Hamel和Heyde(2010)以及Hamel、Heyde和Rudloff(2013)所考虑的集值风险度量的关系。
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英文标题：
《Multivariate risk measures: a constructive approach based on selections》
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作者：
Ignacio Cascos and Ilya Molchanov
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最新提交年份：
2016
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
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 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), Hamel and Heyde (2010), and Hamel, Heyde and Rudloff (2013).
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PDF链接：
https://arxiv.org/pdf/1301.1496
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