英文标题：
《Spatial risk measures and rate of spatial diversification》
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作者：
Erwan Koch
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最新提交年份：
2019
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英文摘要：
  An accurate assessment of the risk of extreme environmental events is of great importance for populations, authorities and the banking/insurance/reinsurance industry. Koch (2017) introduced a notion of spatial risk measure and a corresponding set of axioms which are well suited to analyze the risk due to events having a spatial extent, precisely such as environmental phenomena. The axiom of asymptotic spatial homogeneity is of particular interest since it allows one to quantify the rate of spatial diversification when the region under consideration becomes large. In this paper, we first investigate the general concepts of spatial risk measures and corresponding axioms further and thoroughly explain the usefulness of this theory for both actuarial science and practice. Second, in the case of a general cost field, we give sufficient conditions such that spatial risk measures associated with expectation, variance, Value-at-Risk as well as expected shortfall and induced by this cost field satisfy the axioms of asymptotic spatial homogeneity of order $0$, $-2$, $-1$ and $-1$, respectively. Last but not least, in the case where the cost field is a function of a max-stable random field, we provide conditions on both the function and the max-stable field ensuring the latter properties. Max-stable random fields are relevant when assessing the risk of extreme events since they appear as a natural extension of multivariate extreme-value theory to the level of random fields. Overall, this paper improves our understanding of spatial risk measures as well as of their properties with respect to the space variable and generalizes many results obtained in Koch (2017).
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中文摘要：
准确评估极端环境事件的风险对人口、当局和银行/保险/再保险行业都非常重要。科赫（2017）引入了空间风险度量的概念和一套相应的公理，这些公理非常适合分析由于具有空间范围的事件而产生的风险，例如环境现象。渐近空间同质性公理尤其令人感兴趣，因为它允许人们在考虑的区域变大时量化空间多样化的速度。在本文中，我们首先研究了空间风险度量的一般概念和相应的公理，并深入解释了该理论对精算科学和实践的有用性。其次，在一般成本场的情况下，我们给出了与期望、方差、风险值以及期望短缺相关的空间风险度量满足0$、2$、1$和1$阶渐近空间齐性公理的充分条件。最后但并非最不重要的是，在代价场是最大稳定随机场函数的情况下，我们提供了函数和最大稳定场的条件，以确保后者的性质。最大稳定随机场在评估极端事件风险时是相关的，因为它们是多元极值理论在随机场水平上的自然延伸。总体而言，本文提高了我们对空间风险度量及其空间变量性质的理解，并概括了Koch（2017）的许多结果。
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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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