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## Earthquake Size Distribution and Earthquake Insurance

Yan Y. Kagan

Published 1997, SCEC Contribution #289

The distribution of earthquake seismic moment M is a Pareto (power-law) type with the exponent B=2/3 for shallow earthquakes. To ensure a finite total deformation energy, the distribution has to be modified for the largest earthquakes by introducing either a cutoff at Mmaz or an exponential taper. Analysis of global seismicity suggests that both parameters Mmaz do not change in a statistically significant way over continental areas and tectonic plate boundaries. Thus, very large earthquakes are possible in practically any urbanized areas. We present evidence that the statistical distribution of losses due to large earthquakes has a power-law (Pareto) tail with an exponent value less than 1.0: i.e., the distribution is heavy-tailed. If this statement is true, the earthquake average loss is controlled by the largest earthquakes. Neither the distribution of earthquake size at the maximum, nor the distribution of maximum losses is well known. This implies that insurance premiums can be determined only with significant uncertainty. We simulate the insurance ruin potential for three earthquake loss distributions: exponential, Pareto with exponent 3/2, and Pareto with exponent 2/3. The possibility of catastrophic losses due to great earthquakes suggests that the probabilities of the ruin of insurance companies are unacceptably high, unless the risk reserves are equal to or exceed the maximum possible loss. Although we do not give practical suggestions for earthquake insurance in the paper, these results point out the mathematical and geophysical constraints that insurance should operate within

Key Words
size distribution, geologic hazards, seismicity, earthquakes, seismic risk

Citation
Kagan, Y. Y. (1997). Earthquake Size Distribution and Earthquake Insurance. Communications in Statistics: Stochastic Models, 13(4), 775-797. doi: 10.1080/15326349708807451.