Title: Reduction of Uncertainty in Post-Event Seismic Loss Estimates Using Observation Data and Bayesian Updating
Description: The insurance industry relies on both commercial and in-house software packages to quantify financial risk to natural hazards. For earthquakes, the initial loss estimates from the industry’s catastrophe risk (CAT) models are based on the probabilistic damage a building would sustain due to a catalog of simulated earthquake events. Based on the occurrence rates of the simulated earthquake events, an exceedance probability (EP) curve is calculated, which provides the probability of exceeding a specific loss threshold. Initially these loss exceedence probabilities help a company decide what insurance policies are most cost efficient. In addition they can also provide insights into loss predictions in the event that an actual natural disaster takes place, thus the insurance company is prepared to pay out their insured parties the necessary amount. However, there is always an associated uncertainty with the loss calculations produced by these models. The goal of this research is to reduce this uncertainty by using Bayesian inference with real time earthquake data to calculate an updated loss.

Bayes theory is an iterative process that modifies the loss distribution with every piece of incoming information. The posterior updates are calculated by multiplying a baseline prior distribution with a likelihood function and normalization factor. The first prior is the initial loss distribution from the simulated events database before any information about a real earthquake is available. The crucial step in the update procedure is defining a likelihood function that establishes a relative weight for each simulated earthquake, relating how alike or dislike the attributes of a simulated earthquake are to those of a real earthquake event. To define this likelihood function, the general proposed approach is to quantify real time earthquake attributes such as magnitude, location, building tagging and damage, and compare them to an equivalent value for each simulated earthquake from the CAT model database. In order to obtain the simulated model parameters, the catastrophe risk model is analyzed for different building construction types, such as steel and reinforced concrete.

For every model case, the loss, peak ground acceleration per building and simulated event magnitude and locations are recorded. Next, in order to calculate the real earthquake attributes, data was collected for three case studies, the 7.1 magnitude 1997 Punitaqui, the 8.8 magnitude 2010 Chile earthquake and the 6.7 magnitude 1994 Northridge earthquake. For each of these real earthquake events, the magnitude, location, peak ground acceleration at every available accelerometer location, building tagging and qualitative damage descriptions were recorded. Once the data was collected for both the real and simulated events, they were quantified so they could be compared on equal scales. Using the quantified parameter values, a likelihood function was defined for each update step. In general, as the number of updates increased, the loss estimates tended to converge to a steady value for both the medium and large event. In addition, the loss for the 6.7 and 7.1 event converged to a smaller value than that of the 8.8 event.

The proposed methodology was only applied to earthquakes, but is broad enough to be applied to any type of peril.