Time-dependent Earthquake Risk Modelling

如今，在科学界和(再)保险业，地震往往会相互作用，这一点已经得到了很好的证实。因此，在巨灾模型中经常使用的与时间无关的方法不能完全捕捉实际的地震发生和相关的风险。最近的事件表明，地震往往在空间和时间上聚集，例如2011年坎特伯雷地震序列，而余震序列可以在数十年内增加当地的地震活动，例如在2011年东北地震之后。WRN和Willis Re已经开始与Temblor.inc.共同开展一项研究项目，以期更好地量化大地震后的风险。这使我们能够将我们的模型从捕捉地震频率和风险的历史长期平均观点转变为更好地捕捉新应力的前瞻性模型，从而对重大事件后的预期情况进行评级。这是通过修改模型(默认情况下被建模为独立事件)中的假设地震率来实现的，该模型直接影响PML估计，影响与购买的垂直容量和再保险计划的结构相关的再保险决策。在现实中，问题甚至更加复杂，因为在大事件发生后，将产生广泛的余震序列，事件相互依赖(即在空间和时间上都是聚集的)。预计发生这些地震的地区与任何给定事件的地震工作估计的压力增加的地区很大程度上相关。其中许多余震将是小规模的，尽管其中一些也将是破坏性的，正如我们在最近的一些大地震中看到的(例如，2011年东北、2011年克赖斯特彻奇EQ序列、2018年龙目岛(印度尼西亚)地震)。因此，该博士项目将着眼于将完整余震序列及其相关事件的生成纳入灾难模拟框架中，并将其纳入随机事件集。不仅捕捉与地震相关的速率变化，而且实际上整个集群事件集还将使我们进一步前瞻性地看待模型，不仅对垂直容量和PML估计有直接影响，而且对AEP曲线、总覆盖范围和小时数条款也有直接影响。

It is nowadays well established in the scientific community and (re)insurance industry that earthquakes tend to interact with each other. Hence, time-independent approaches often used in catastrophe models are not able to fully capture the actual earthquake occurrence and the associated risk. Recent events have shown that earthquakes tend to cluster in space and time, e.g. the 2011 Canterbury earthquake sequence, and that aftershock sequences can increase the local seismicity for decades, e.g. following the 2011 Tohoku earthquake. WRN & Willis Re have already embarked on a research project with Temblor.inc towards the better quantification of the risk following a major earthquake. This has allowed us to transform our models from capturing the historical long-term average view of earthquake frequency and hazard, to forward-looking models that better capture the new stress, and as a result, rate conditions expected after a major event. This is done by revising the assumed earthquake rates within the models (which are by default modelled as independent events) with direct implications for the PML estimates, affecting reinsurance decisions related to the amount of vertical capacity purchased and structuring of reinsurance programs.In reality, the issue is even more complex due to the fact that following a major event, an extensive aftershock sequence will be produced with events dependent on each other (i.e. clustered in both space and time). The areas where these events are expected to happen are largely correlated with areas of stress increase estimated by the Temblor work for any given event. Many of these aftershocks will be of small magnitude, though a number of them will also be damaging as we saw in a number of recent large earthquakes (e.g. 2011 Tohoku, 2011 Christchurch EQ sequence, 2018 Lombok (Indonesia) events). This PhD project will thus look at incorporating within a catastrophe modelling framework the generation of the full aftershock sequence and its associated events within the stochastic event set. Capturing not only the rate changes associated with an earthquake, but actually the full clustered event set will also us to take the forward-looking view of the models one step further, with direct implications not only on vertical capacity and PML estimates, but also on the AEP curve, aggregate covers and hours clauses.