Optimal Insurance For Catastrophic Risk: Theory And Application To Nuclear Corporate Liability

We analyze the optimal insurance coverage for high severity-low probability accidents, both from theoretical and applied standpoints. Such accidents qualify as catastrophic when their risk premium is a non-negligible proportion of the victims' wealth, although the probability of occurrence is very small. We show that this may be the case when the individual's absolute risk aversion is very large in the accident case. We characterize the optimal insurance contract firstly for an individual, and secondly for a firm that may be at the origin of an accident that affects the whole population. The optimal indemnity schedule converges to a limit when the probability of the accident tends to zero. In the case of corporate civil liability, this limit schedule is a straight deductible contract that corresponds to an indemnification of victims ranked in order of priority according to the severity of their losses. We also show that the size of the deductible depends on the individuals' risk aversion and also on the cost of contingent risk capital that is required to sustain the indemnity payment, should an accident occur. The empirical part of the paper is an application of these general principles to the case of nuclear accidents. Large scale nuclear accidents are typical examples of high severity-low probability risks. We calibrate a model on French data in order to estimate the optimal liability ceiling of an electricity producer in the nuclear energy sector. We use data drawn from the cat-bond markets to estimate the cost of contingent capital for low probability events, and we show that the minimal corporate liability adopted in 2004 through the revision of the Paris Convention is probably lower than the level that would correspond to an optimal risk coverage of the population.