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A numerical approach for a class of risk-sharing problems

  • Carlier, G.
  • Lachapelle, A.
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    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.

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    File URL: http://www.sciencedirect.com/science/article/B6VBY-51JF89H-1/2/2ca2eb37c8515199b47ae34bf13a8e25
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    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 47 (2011)
    Issue (Month): 1 (January)
    Pages: 1-13

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    Handle: RePEc:eee:mateco:v:47:y:2011:i:1:p:1-13
    Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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    1. Galichon, Alfred & Dana, Rose-Anne & Carlier, Guillaume, 2012. "Pareto efficiency for the concave order and multivariate comonotonicity," Economics Papers from University Paris Dauphine 123456789/9713, Paris Dauphine University.
    2. Carlier, Guillaume & Dana, Rose-Anne, 2003. "Core of convex distortions of a probability," Economics Papers from University Paris Dauphine 123456789/5446, Paris Dauphine University.
    3. Jouini, Elyès & Schachermayer, Walter & Touzi, Nizar, 2008. "Optimal Risk Sharing for Law Invariant Monetary Utility Functions," Economics Papers from University Paris Dauphine 123456789/361, Paris Dauphine University.
    4. Dana, Rose-Anne & Carlier, Guillaume, 2006. "Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraints," Economics Papers from University Paris Dauphine 123456789/5392, Paris Dauphine University.
    5. 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.
    6. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    7. 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 26, July.
    8. Dana, Rose-Anne & Carlier, Guillaume, 2008. "Two-Persons Efficient Risk-Sharing and Equilibria for Concave Law-Invariant Utilities," Economics Papers from University Paris Dauphine 123456789/2348, Paris Dauphine University.
    9. Carlier, G. & Dana, R. A., 2003. "Core of convex distortions of a probability," Journal of Economic Theory, Elsevier, vol. 113(2), pages 199-222, December.
    10. G. Carlier & R. Dana, 2008. "Two-persons efficient risk-sharing and equilibria for concave law-invariant utilities," Economic Theory, Springer, vol. 36(2), pages 189-223, August.
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