Robust Modeling of Earthquake Catastrophe Risk for Insurance: An Integrated Approach Incorporating Active Faults and an Epidemic-Type Model

Typically, the assessment of seismic risk premium relies heavily on the spatiotemporal model of seismic events. While most actuarial approaches concentrate on models with simpler dynamics, such as the homogeneous Poisson model, this research article examines a more sophisticated modeling approach utilizing the historical catalog as a branching process, specifically the epidemic-type aftershock sequence model. Based on the stochastic declustering of the events, the probability distribution function of the maximum magnitude of the background events and their descendants is used as input for the premium rating process. Since historical catalogs only provide a small amount of information compared to the properties of seismic faults, the latter are incorporated to estimate the seismic risk. A case study focusing on the region of Greece is presented, which aligns with findings from the reinsurance market in terms of expected loss. Contrary to the standard formula of Solvency II, we propose a lower solvency capital requirement by employing value at risk as the designated risk measure.