Optimal insurance for catastrophic risk: theory and application to nuclear corporate liability

This paper analyzes the optimal insurance for low probability - high severity accidents, such as nuclear catastrophes, both from theoretical and applied standpoints. We show that the risk premium of such catastrophic events may be a non-negligible proportion of individuals' wealth when the index of absolute risk aversion is sufficiently large in the accident state, and we characterize the optimal asymptotic insurance coverage when the probability of the accident tends to zero. In the case of the limited liability of an industrial firm that may cause large scale damage, the limit corporate insurance contract corresponds to a straight deductible indemnification rule, in which victims are ranked according to the severity of their losses. As an application of these general principles, we consider the optimal corporate liability insurance for nuclear risk, in a setting where the risk is transferred to financial markets through catastrophe bonds. A model calibrated with French data allows us to estimate the optimal liability of a nuclear energy producer. This leads us to the conclusion that the lower limit adopted in 2004 through the revision of the Paris Convention is probably inferior to the socially optimal level.