英文标题：
《A theory for combinations of risk measures》
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作者：
Marcelo Brutti Righi
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最新提交年份：
2020
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英文摘要：
We study combinations of risk measures under no restrictive assumption on the set of alternatives. We develop and discuss results regarding the preservation of properties and acceptance sets for the combinations of risk measures. One of the main results is the representation for resulting risk measures from the properties of both alternative functionals and combination functions. To that, we build on the development of a representation for arbitrary mixture of convex risk measures. In this case, we obtain a penalty that recalls the notion of inf-convolution under theoretical measure integration. As an application, we address the context of probability-based risk measurements for functionals on the set of distribution functions. We develop results related to this specific context. We also explore features of individual interest generated by our framework, such as the preservation of continuity properties, the representation of worst-case risk measures, stochastic dominance and elicitability. We also address model uncertainty measurement under our framework and propose a new class of measures for this task.
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中文摘要：
我们研究了在非限制性假设条件下的风险度量组合。我们制定并讨论了有关财产保护和风险度量组合验收集的结果。主要结果之一是从替代函数和组合函数的性质来表示结果风险度量。为此，我们建立在凸风险度量的任意混合表示的基础上。在这种情况下，我们得到了一个惩罚，它在理论测度积分下唤起了inf卷积的概念。作为一个应用，我们讨论了分布函数集上泛函基于概率的风险度量。我们制定了与这一特定背景相关的结果。我们还探讨了我们的框架所产生的个人利益的特征，如连续性的保持、最坏情况风险度量的表示、随机优势和可诱导性。我们还讨论了在我们的框架下的模型不确定性度量，并为此任务提出了一类新的度量。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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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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