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Financial equilibrium with non-linear valuations

Classical Arrow Debreu equilibria employ budget feasibility to require individuals to ensure excess supplies to be nonnegative in value using the single equilibrium price system for valuation purposes. Yet by the selection of state contingent prices, they seek excess supplies that are nonnegative in each component, and not just the value. A financial equilibrium, on the other hand, defines acceptable economic risks as excess supplies that are nonnegative in value for a number of prespecified valuation price systems. The collection of prespecified valuation price systems may be referred to as features for which clearing is sought. The number of features will generally be less than the number of states. It is then shown that by also defining budget feasibility nonlinearly one may construct a financial equilibrium with fewer securities than there are features to be cleared.