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The first contribution of this article is to provide a framework, a model together with a corresponding equilibrium notion, suitable for the study of the interaction between insurance and dynamic financial markets. Our central result is that in equilibrium risk-averse agents purchase full insurance coverage, despite unfair insurance prices. We identify three conditions that explain this result: (1) insurance contracts are priced competitively, (2) financial prices include a risk premium only for undiversifiable risk, and (3) financial markets are effectively complete. An implication is that in this model disasters can be insured by fully assessable stock insurance companies.