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The calculation of expected loss using probabilistic seismic hazard

California Department of Conservation Division of Mines and Geology, 801 K Street, MS 13-35, Sacramento, California 95814-3531

Abstract

The formulas for the estimation of expected loss from probabilistic seismic hazard are presented systematically by using the basics of calculating expected values and the concept of distributing the total loss between the insurer and the insured. The conversion from acceleration to intensity and then to loss factor (the ratio of damage value to the property value) is applied in the calculation. The seismic hazard used in the loss calculation is for four locations in California. These locations are representative of high and low hazards in California and of the two most populated areas in northern and southern California. The calculated loss values show a strong dependence on the hazard and the soil conditions. The deaggregation of total loss with respect to intensity, acceleration, and loss factor shows that a greater portion of the total loss in the high-hazard region is from large intensities and accelerations compared with the low-hazard region. The deaggregation with respect to loss factor reveals that most of the loss is from loss factors below 15-20%, even for the high-hazard regions. This result has a significant impact on the amount of the loss that is greater than the deductible. The calculation of loss to the insurer shows that a mere 5% deductible reduces the loss to the insurer by 40-50% for a high-hazard region and by more than that for a low-hazard region. Underinsurance and inflation have the effect of increasing the loss to the insurer but are less significant than the effect of deductible in reducing the loss to the insurer. These calculations suggest that updating the relation converting ground motion to loss factor is critical. In addition, the correction for soil condition needs to be calibrated with more recent strong-motion and earthquake damage data.

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