Seismicity in Italy: The Problem of Insurance of the Real Estate Property

After few considerations on the damage caused by earthquakes and on how different countries address the consequent economic implications, we consider the problem of the insurance of the buildings for the earthquake risk. The risk for insurance purposes may tentatively be estimated with the random walk (RW) method since the earthquakes are measured in the new scale of the seismic moment. The method is addressed to the case when only forward steps are possible and the probability density function (pdf) of their occurrence, that is the waiting time pdf, is formulated to lead to a Mittag Leffler function. It is seen that when pdf of the sizes of the steps is a negative power law then the integral equation leading to the solution of the problem is reduced to a fractional order differential equation with two different orders of fractional differentiation. The solution is then found in closed form in the time domain using the Laplace Transform. It is finally shown how the theory may tentatively model the risk of real estate insurance providers to cover the cost of the damage caused by earthquakes and consequently guide the estimate of the premiums for the risk.