The calculation of expected loss using probabilistic seismic hazard

The formulas for the estimation of expected loss from probabilistic seismic hazard are presented systematically by using the basics of calculating exp ected values and the concept of distributing the total loss between the ins urer and the insured. The conversion from acceleration to intensity and the n to loss factor (the ratio of damage value to the property value) is appli ed in the calculation. The seismic hazard used in the loss calculation is f or four locations in California, These locations are representative of high and low hazards in California and of the two most populated areas in north ern and southern California. The calculated loss values show a strong depen dence on the hazard and the soil conditions. The deaggregation of total los s with respect to intensity, acceleration, and loss factor shows that a gre ater portion of the total loss in the high-hazard region is from large inte nsities and accelerations compared with the low-hazard region. The deaggreg ation with respect to loss factor reveals that most of the loss is from los s 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 dedu ctible. The calculation of loss to the insurer shows that a mere 5% deducti ble 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 hav e 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 c alculations suggest that updating the relation converting ground motion to loss factor is critical. In addition, the correction for soil condition nee ds to be calibrated with more recent strong-motion and earthquake damage da ta.