Extreme values in business interruption insurance

The size distribution of yearly claims in the French business interruption insurance branch is a Pareto law with an extremely long tail. The behavior of that law reflects the fact that the total value of yearly claims is dominated by a small number of huge claims. The estimated characteristic exponent of the tail is very close to one. The article analyzes the consequences of that particular value on the actuarial risk covered by the insurance and the reinsurance companies.