英文标题：
《Surplus-invariant risk measures》
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作者：
Niushan Gao, Cosimo Munari
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最新提交年份：
2018
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英文摘要：
  This paper presents a systematic study of the notion of surplus invariance, which plays a natural and important role in the theory of risk measures and capital requirements. So far, this notion has been investigated in the setting of some special spaces of random variables. In this paper we develop a theory of surplus invariance in its natural framework, namely that of vector lattices. Besides providing a unifying perspective on the existing literature, we establish a variety of new results including dual representations and extensions of surplus-invariant risk measures and structural results for surplus-invariant acceptance sets. We illustrate the power of the lattice approach by specifying our results to model spaces with a dominating probability, including Orlicz spaces, as well as to robust model spaces without a dominating probability, where the standard topological techniques and exhaustion arguments cannot be applied.
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中文摘要：
本文对盈余不变性的概念进行了系统的研究，盈余不变性在风险度量和资本要求理论中起着天然而重要的作用。到目前为止，这一概念已经在一些特殊的随机变量空间中得到了研究。在本文中，我们发展了一个自然框架下的剩余不变性理论，即向量格的剩余不变性理论。除了对现有文献提供统一的观点外，我们还建立了各种新的结果，包括剩余不变风险度量的对偶表示和扩展以及剩余不变接受集的结构结果。我们通过将结果指定给具有支配概率的模型空间（包括Orlicz空间）以及不具有支配概率的鲁棒模型空间（其中无法应用标准拓扑技术和穷举参数），来说明格方法的威力。
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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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