By Thompson S.
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Assume that all homes in an earthquake-prone area are equally resistant to damage such that the insurance premium, z, is the same for each structure. Further assume that an insurer has $A dollars in current surplus and wants to determine the number of policies it can write and still satisfy its survival constraint. Then, the maximum number of policies, n, satisfying the survival constraint is: Whether the company will view the earthquake risk as insurable depends on whether the fixed cost of marketing and issuing policies is sufficiently low to make a positive expected profit.
Topics: Annual Review of North American Natural Catastrophes 2002. Atwater, B. and Hemphill-Haley, E. (1997). Recurrence intervals for great earthquakes of the past 3,500 years at northeastern Willapa Bay, Washington. S. Geological Survey Professional Paper 1576. 108p. Beaulieu, J. (2001). Personal communication with Don Windeler, April 30, 2001. California Earthquake Authority (2003). Weekly Policy and Premium Status Report, July 31, 2003. , Wang, Y, and Wong, I. eds. (2000). Consensus statement.
In general, insurance markets flourish when companies can issue a large number of policies whose losses are spatially and otherwise independent. The portfolio follows the law of large numbers, and is thus predictable. This law states that for a series of independent and identically distributed random variables, the variance around the mean of the random variables decreases as the number of variables increases. Losses from natural hazards do not follow the law of large numbers, as they are not independent.