# Restrictions and identification in a multidimensional risk-sharing problem

*Marwan Aloqeili* (),
*G. Carlier* () and
*I. Ekeland* ()

*Economic Theory*, 2014, vol. 56, issue 2, 409-423

**Abstract:**
We consider $$H$$ H expected utility maximizers that have to share a risky aggregate multivariate endowment $$X\in {\mathbb {R}}^{N}$$ X ∈ R N and address the following two questions: does efficient risk-sharing imply restrictions on the form of individual consumptions as a function of $$X$$ X ? Can one identify the individual utility functions from the observation of the risk-sharing? We show that when $$H\ge \frac{2N}{N-1}$$ H ≥ 2 N N - 1 efficient risk sharings have to satisfy a system of nonlinear PDEs. Under an additional rank condition, we prove an identification theorem. Copyright Springer-Verlag Berlin Heidelberg 2014

**Keywords:** Multidimensional risk-sharing; Restrictions; Identification; C10; D61; D81 (search for similar items in EconPapers)

**Date:** 2014

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**Persistent link:** https://EconPapers.repec.org/RePEc:spr:joecth:v:56:y:2014:i:2:p:409-423

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**DOI:** 10.1007/s00199-013-0791-x

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