Duality for Set-Valued Measures of Risk
Duality for Set-Valued Measures of Risk
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DOI：
10.1137/080743494
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发表时间：
2010-02
期刊：
影响因子：
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通讯作者：
A. Hamel;F. Heyde
中科院分区：
文献类型：
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作者：
A. Hamel;F. Heyde
推广了Jouini，Meddeb和Touzi的方法[Finance Stoch，8(2004)，pp.531-552]，我们定义了风险的集值(凸)度量及其接受集，并给出了对偶表示定理。引入了一个标量化的概念，它具有参考工具组合的内部价格的意义。利用原始描述和对偶描述，我们引入了集值风险度量的新例子，例如集值上期望、在险价值、平均在险价值和熵风险度量。
Extending the approach of Jouini, Meddeb, and Touzi [Finance Stoch., 8 (2004), pp. 531-552] we define set-valued (convex) measures of risk and their acceptance sets, and we give dual representation theorems. A scalarization concept is introduced that has a meaning in terms of internal prices of portfolios of reference instruments. Using primal and dual descriptions, we introduce new examples for set-valued measures of risk, e.g., set-valued upper expectations, value at risk, average value at risk, and entropic risk measure.