英文标题：
《Extremal dependence and spatial risk measures for insured losses due to
extreme winds》
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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：
A meticulous assessment of the risk of impacts associated with extreme wind events is of great necessity for populations, civil authorities as well as the insurance industry. Using the concept of spatial risk measure and related set of axioms introduced by Koch (2017, 2019), we quantify the risk of losses due to extreme wind speeds. The insured cost due to wind events is proportional to the wind speed at a power ranging typically between 2 and 12. Hence we first perform a detailed study of the correlation structure of powers of the Brown-Resnick max-stable random fields and look at the influence of the power. Then, using the latter results, we thoroughly investigate spatial risk measures associated with variance and induced by powers of max-stable random fields. In addition, we show that spatial risk measures associated with several classical risk measures and induced by such cost fields satisfy (at least part of) the previously mentioned axioms under conditions which are generally satisfied for the risk of damaging extreme wind speeds. In particular, we specify the rates of spatial diversification in different cases, which is valuable for the insurance industry.
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中文摘要：
对与极端风事件相关的影响风险进行细致的评估对于人口、民政部门以及保险业来说都是非常必要的。利用科赫（2017、2019）提出的空间风险度量概念和相关公理集，我们量化了极端风速造成的损失风险。风力事件导致的保险成本与功率范围通常在2到12之间的风速成比例。因此，我们首先对Brown-Resnick极大稳定随机场的幂相关结构进行了详细的研究，并考察了幂的影响。然后，利用后一个结果，我们深入研究了与方差相关的空间风险度量以及由最大稳定随机场的幂引起的空间风险度量。此外，我们还表明，在通常满足破坏极端风速风险的条件下，与几个经典风险度量相关的空间风险度量以及由此类成本场诱导的空间风险度量满足（至少部分）上述公理。特别是，我们指定了不同情况下的空间多元化率，这对保险业很有价值。
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分类信息：

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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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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