Restrictions and identification in a multidimensional risk-sharing problem |
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Authors: | M Aloqeili G Carlier I Ekeland |
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Institution: | 1. Department of Mathematics, Birzeit University, P.O. Box 14, Birzeit, Palestine 2. CEREMADE, UMR CNRS 7534, Université Paris Dauphine, Pl. de Lattre de Tassigny, 75775?, Paris Cedex 16, France
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Abstract: | We consider $H$ expected utility maximizers that have to share a risky aggregate multivariate endowment $X\in {\mathbb {R}}^{N}$ 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 $H\ge \frac{2N}{N-1}$ 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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