Optimality of Incomplete Markets

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Abstract
In a static exchange economy where the traders′ initial endowments are risky, the optimality of the financial structure is studied when markets are incomplete. Only financial structures with the same number of assets are compared. A market structure is optimal, when, in a particular economy, it yields an allocation of risks which cannot be Pareto-dominated through the implementation of any other market structure. In a linear Gaussian setup, the optimal market structures are shown to span an eigenspace of a matrix which combines the risk exposures of the participants in the market, approximately weighted by a measure of their risk aversions.
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