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On the C-property and $w^*$-representations of risk measures

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  • Niushan Gao
  • Foivos Xanthos

Abstract

We identify a large class of Orlicz spaces $X$ for which the topology $\sigma(X,X_n^\sim)$ fails the C-property introduced in [7]. We also establish a variant of the C-property and use it to prove a $w^*$-representation theorem for proper convex increasing functionals on dual Banach lattices that satisfy a suitable version of Delbaen's Fatou property. Our results apply, in particular, to risk measures on all Orlicz spaces over $[0,1]$ which is not $L_1[0,1]$.

Suggested Citation

  • Niushan Gao & Foivos Xanthos, 2015. "On the C-property and $w^*$-representations of risk measures," Papers 1511.03159, arXiv.org, revised Sep 2016.
    • Handle: RePEc:arx:papers:1511.03159
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    References listed on IDEAS

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    1. Freddy Delbaen, 2009. "Risk Measures For Non‐Integrable Random Variables," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 329-333, April.
    2. Keita Owari, 2013. "On the Lebesgue Property of Monotone Convex Functions," CARF F-Series CARF-F-317, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print halshs-00176522, HAL.
    4. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    5. 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.
    6. repec:dau:papers:123456789/342 is not listed on IDEAS
    7. Patrick Cheridito & Tianhui Li, 2009. "Risk Measures On Orlicz Hearts," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 189-214, April.
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