The Insurance of Low Probability Events.

We consider a model in which the agent faces two independant risks of losswith different probabilities of occurence and (possibly) different levels of potential loss. We show that it is optimal to select a deductable for the low probability event that is not larger than the optimal deductable for the other risk. This result holds for any preference functional that satisfies the second-order stochastic dominance property. When the expected loss is the same for the two risks, i.e. when the low probability event is also "catastrophic", it is never optimal not to insure the catastrophic risk when some insurance is purchased for the other risk. We also obtain some additional properties of the optimal insurance strategy in the case of expected utility, or in the case of Yaari's dual theory.