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On optimal allocation of risk vectors

  • Kiesel, Swen
  • Rüschendorf, Ludger
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    In this paper we extend results on optimal risk allocations for portfolios of real risks w.r.t. convex risk functionals to portfolios of risk vectors. In particular we characterize optimal allocations minimizing the total risk as well as Pareto optimal allocations. Optimal risk allocations are shown to exhibit a worst case dependence structure w.r.t. some specific max-correlation risk measure and they are comonotone w.r.t. a common worst case scenario measure. We also derive a new existence criterion for optimal risk allocations and discuss some examples.

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    File URL: http://www.sciencedirect.com/science/article/B6V8N-5086079-1/2/59f04a9a6a62700f015cf9c9a2174604
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    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 47 (2010)
    Issue (Month): 2 (October)
    Pages: 167-175

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    Handle: RePEc:eee:insuma:v:47:y:2010:i:2:p:167-175
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505554

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    1. E. Jouini & W. Schachermayer & N. Touzi, 2008. "Optimal Risk Sharing For Law Invariant Monetary Utility Functions," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 269-292.
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    7. Alfred Galichon & Ivar Ekeland & Marc Henry, 2009. "Comonotonic measures of multivariates risks," Working Papers hal-00401828, HAL.
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    9. Zephyr, 2010. "The city," City, Taylor & Francis Journals, vol. 14(1-2), pages 154-155, February.
    10. Beatrice Acciaio, 2007. "Optimal risk sharing with non-monotone monetary functionals," Finance and Stochastics, Springer, vol. 11(2), pages 267-289, April.
    11. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    12. Ludkovski, Michael & Rüschendorf, Ludger, 2008. "On comonotonicity of Pareto optimal risk sharing," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1181-1188, August.
    13. Damir Filipović & Gregor Svindland, 2008. "Optimal capital and risk allocations for law- and cash-invariant convex functions," Finance and Stochastics, Springer, vol. 12(3), pages 423-439, July.
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