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Subgradients of law-invariant convex risk measures on L

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  • Svindland Gregor

Abstract

We introduce a generalised subgradient for law-invariant closed convex risk measures on L1 and establish its relationship with optimal risk allocations and equilibria. Our main result gives sufficient conditions ensuring a non-empty generalised subgradient.

Suggested Citation

  • Svindland Gregor, 2009. "Subgradients of law-invariant convex risk measures on L," Statistics & Risk Modeling, De Gruyter, vol. 27(2), pages 169-199, December.
  • Handle: RePEc:bpj:strimo:v:27:y:2009:i:2:p:169-199:n:4
    DOI: 10.1524/stnd.2009.1040
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    References listed on IDEAS

    as
    1. 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.
    2. repec:dau:papers:123456789/342 is not listed on IDEAS
    3. 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, April.
    4. Andrzej Ruszczyński & Alexander Shapiro, 2006. "Optimization of Convex Risk Functions," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 433-452, August.
    5. Damir Filipović & Michael Kupper, 2008. "Equilibrium Prices For Monetary Utility Functions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(03), pages 325-343.
    6. Rose‐Anne Dana, 2005. "A Representation Result For Concave Schur Concave Functions," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 613-634, October.
    7. Patrick Cheridito & Tianhui Li, 2009. "Risk Measures On Orlicz Hearts," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 189-214, April.
    8. Beatrice Acciaio, 2007. "Optimal risk sharing with non-monotone monetary functionals," Finance and Stochastics, Springer, vol. 11(2), pages 267-289, April.
    9. Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," Finance and Stochastics, Springer, vol. 9(2), pages 269-298, April.
    10. Freddy Delbaen, 2009. "Risk Measures For Non‐Integrable Random Variables," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 329-333, April.
    11. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    12. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print halshs-00176522, HAL.
    13. repec:dau:papers:123456789/361 is not listed on IDEAS
    14. Barrieu, Pauline & El Karoui, Nicole, 2005. "Inf-convolution of risk measures and optimal risk transfer," LSE Research Online Documents on Economics 2829, London School of Economics and Political Science, LSE Library.
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