Restrictions and identification in a multidimensional risk-sharing problem.

Summary 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.