Financial Markets for Unknown Risks

An economy faces an unknown individual risk, such as the health effects of recently discovered environmental hazard. Opinions may be widely different about the distribution of risks across the population. We study financial markets that suffice to reach efficient allocations in this situation. The problem is formalized in a general equilibrium economy with incomplete markets for individual and collective uncertainty. We show that ignorance of the probabilities describing individual risk leads to collective risk. Introducing an array of mutual insurance policies and of Arrow securities is shown to lead to Arrow-Debreu competitive allocations. By combining insurance contracts for individual risks and securities markets for collective risks, the proposed institutional framework economizes significantly on the number of markets required for efficiency. The computational complexity of a market equilibrium is reduced from an NP-complete (i.e. intractable) problem to one which depends polynomially on the number of households