Time-dependent Earthquake Risk Modelling

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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.