Necessary and Sufficient Informational Conditions for Pareto-Efficient Risk Sharing in Incomplete Markets

Although, the marginal Lagrange conditions for Pareto-optimal risk-sharing are known, the precise informational requirements of the risk- sharing contracts are not known. This paper determines the minimal structure of such information under heterogeneous beliefs and the functional nature of these contracts. Sufficient statistics play a dominant role in the development. Since security markets are typically not complete in the Arrow-Debreu sense, the minimal information requirements indicate the minimal spanning conditions for optimal risk-sharing. If the minimal spanning does not obtain and the incompleteness is informational and not institutional, there is social value in additional contractual information.