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A numerical approach for a class of risk-sharing problems

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  • Carlier, G.
  • Lachapelle, A.

Abstract

This paper deals with risk-sharing problems between many agents, each of whom having a strictly concave law invariant utility. In the special case where every agent's utility is given by a concave integral functional of the quantile of her individual endowment, we fully characterize the optimal risk-sharing rules. When there are many agents, these rules cannot be computed analytically. We therefore give a simple convergent algorithm and illustrate it on several examples.

Suggested Citation

  • Carlier, G. & Lachapelle, A., 2011. "A numerical approach for a class of risk-sharing problems," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 1-13, January.
    • Handle: RePEc:eee:mateco:v:47:y:2011:i:1:p:1-13
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    References listed on IDEAS

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    7. Hara, Chiaki & Huang, James & Kuzmics, Christoph, 2007. "Representative consumer's risk aversion and efficient risk-sharing rules," Journal of Economic Theory, Elsevier, vol. 137(1), pages 652-672, November.
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    9. G. Carlier & R. Dana, 2008. "Two-persons efficient risk-sharing and equilibria for concave law-invariant utilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(2), pages 189-223, August.
    10. Carlier Guillaume & Dana Rose-Anne, 2006. "Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraints," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-26, July.
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    Cited by:

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    2. Mario Ghossoub, 2015. "Equimeasurable Rearrangements with Capacities," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 429-445, February.
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    4. Ghossoub, Mario, 2011. "Monotone equimeasurable rearrangements with non-additive probabilities," MPRA Paper 37629, University Library of Munich, Germany, revised 23 Mar 2012.
    5. Zuo Quan Xu, 2021. "Moral-hazard-free insurance: mean-variance premium principle and rank-dependent utility theory," Papers 2108.06940, arXiv.org, revised Aug 2022.

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