This paper studies aggregation and a weak form of optimality referring to the p-weakly constrained Pareto efficiency (p-WE) in stochastic finance economies with incomplete markets. We derive a representative agent utility function maximized at equilibrium and a characterization of the set of p-WE allocations. Moreover, we establish the correspondence between the set of competitive equilibrium allocations and the set of p-WE allocations. It is noted that these are accomplished for general time-state utility functions and without restrictions on the initial resource allocations.

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Journal Social Choice and Welfare
Ma, C. (Chenghu), & Zhang, J. (2013). p-Weakly constrained Pareto efficiency and aggregation in incomplete markets. Social Choice and Welfare, 41(3), 605–623. doi:10.1007/s00355-012-0695-x