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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 LΦ(μ) for which the topology σ(LΦ(μ),LΦ(μ)n∼) fails the C†property introduced by Biagini and Frittelli. We also establish a variant of the C†property and use it to prove a w∗†representation theorem for proper convex increasing functionals, satisfying a suitable version of Delbaen's Fatou property, on Orlicz spaces LΦ(μ) with limt→∞Φ(t)t=∞. Our results apply, in particular, to risk measures on all Orlicz spaces LΦ(P) other than L1(P).

Suggested Citation

  • Niushan Gao & Foivos Xanthos, 2018. "On the C†property and w∗†representations of risk measures," Mathematical Finance, Wiley Blackwell, vol. 28(2), pages 748-754, April.
    • Handle: RePEc:bla:mathfi:v:28:y:2018:i:2:p:748-754
    DOI: 10.1111/mafi.12150
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    Citations

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    Cited by:

    1. Felix-Benedikt Liebrich & Marco Maggis & Gregor Svindland, 2020. "Model Uncertainty: A Reverse Approach," Papers 2004.06636, arXiv.org, revised Mar 2022.
    2. Massoomeh Rahsepar & Foivos Xanthos, 2020. "On the extension property of dilatation monotone risk measures," Papers 2002.11865, arXiv.org.
    3. Ruodu Wang & Yunran Wei & Gordon E. Willmot, 2020. "Characterization, Robustness, and Aggregation of Signed Choquet Integrals," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 993-1015, August.
    4. Martin Herdegen & Nazem Khan, 2020. "Mean-$\rho$ portfolio selection and $\rho$-arbitrage for coherent risk measures," Papers 2009.05498, arXiv.org, revised Jul 2021.
    5. Anastasis Kratsios, 2019. "Partial Uncertainty and Applications to Risk-Averse Valuation," Papers 1909.13610, arXiv.org, revised Oct 2019.
    6. Felix-Benedikt Liebrich & Max Nendel, 2020. "Separability vs. robustness of Orlicz spaces: financial and economic perspectives," Papers 2009.09007, arXiv.org, revised May 2021.
    7. Niushan Gao & Foivos Xanthos, 2024. "A note on continuity and consistency of measures of risk and variability," Papers 2405.09766, arXiv.org.

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