Restrictions and identification in a multidimensional risk-sharing problem

Abstract : We consider $H$ expected utility maximizers that have to share a risky aggregate multivariate endowment $X 2 R N$ and address the following two questions: does efficient risk-sharing imply restrictions on the form of individual consumptions as a function of $X$? Can one identify the individual utility functions from the observation of the risk-sharing? We show that when $H 2N N 1$ efficient risk sharings have to satisfy a system of nonlinear PDEs. Under an additional rank condition, we prove an identification theorem.
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Marwan Aloqeili, Guillaume Carlier, Ivar Ekeland. Restrictions and identification in a multidimensional risk-sharing problem. Economic Theory, Springer Verlag, 2014, 56 (2), pp.409 - 423. ⟨10.1007/s00199-013-0791-x⟩. ⟨hal-01521479⟩

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