气候变化中总风暴风险的分布
The distribution of aggregate storm risk in a changing climate
摘要：
极端天气事件造成的经济损失可能会产生灾难性的影响，通常会造成数十亿英镑的损失。虽然个别事件处置的变化对保险业和再保险业都很重要，但这些公司往往关心的是一个季节中构成的总风险。这个项目探讨了当为了反映地球气候的变化而使模型具有时间依赖性时，综合风险度量的统计特性可能会发生怎样的变化。Wald（1945）和Blackwell和Girshick（1947）的历史随机和方程被用来建立事件频率和总风险之间的关系。事件的发生与总风险之间的协方差是总风险的期望值与离差统计量的乘积。此外，一个新的方程（“J方程”）将事件频率和总风险与风暴强度分布形状和离散统计量之间的相关性联系起来。该等式强调了两个变量之间的相关性对于严重程度分布的尺度变化是不变的。该理论应用于2020年挪威气候模型NorESM 2-LM的模拟未来数据集。随着数据观察到所提出的理论，这为这些结果在未来的研究中应用于更广泛的地理区域打开了大门。
英文摘要：
The financial losses from extreme weather events can have a disastrous effect, often costing billions of pounds. While changes in the disposition of individual events is of importance to both the insurance and re-insurance industries, these companies are often concerned with the aggregate risk posed in a season. This project explores how the statistical properties of aggregate risk measures may change when, to reflect the earth's changing climate, models are made time dependent. Historical random sum equations by Wald (1945) and Blackwell and Girshick (1947) are used to develop a relationship between the frequency of events and the aggregate risk. The covariance between the occurrence of events and aggregate risk is found to be the product of the expected value of the aggregate risk and the dispersion statistic. Furthermore, a new equation (the "J-equation") relates the correlation between the frequency of events and aggregate risk to the shape of the distribution of storm intensities and the dispersion statistic. This equation highlights that the correlation between the two variables is invariant to a change in the scale of the severity distribution. The theory is applied to a simulated future dataset from the 2020 Norwegian climate model NorESM2-LM. As the data observes the theory presented, this opens the door for these results to be applied to wider geographical regions in future studies.
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