Catastrophes provide a principal justification for insurance. Traditio
nal conceptions of catastrophes miss three critical elements. (1) Marr
y catastrophes-the liability revolution in the United States, for exam
ple-are not bolts from the blue. Rather, they develop over many years
and result from human activity. (2) Conventional, experienced-based mo
dels for assessing losses often smudge the distinction, so critical fo
r catastrophes, between probability and magnitude of loss. (3) Normal
insurance contracts, with heavy copayments for small losses but little
charge at the margin for large ones, perform poorly when the insured
can tradeoff probability and size of loss-a phenomenon we label distri
bution distortion. Tire structures of optimal insurance contracts are
assessed.