The distinguishing feature of natural-catastrophe risk is claimed to be aggregate risk. Because such risk is encompassed in the general competitive model, it seems to pose no new theoretical challenge. However, that model has markets contingent on exogenous events, while the actual economy seems to be developing mainly markets contingent on the level of total damage. In the context of a model with aggregate risk and endogenous total damage, a notion of competitive markets contingent on total damage is formulated. That notion implies that such markets achieve the same (efficient) risk sharing as markets contingent on exogenous events.