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On closedness of law-invariant convex sets in rearrangement invariant spaces

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  • Made Tantrawan
  • Denny H. Leung

Abstract

This paper presents relations between several types of closedness of a law-invariant convex set in a rearrangement invariant space $\mathcal{X}$. In particular, we show that order closedness, $\sigma(\mathcal{X},\mathcal{X}_n^\sim)$-closedness and $\sigma(\mathcal{X},L^\infty)$-closedness of a law-invariant convex set in $\mathcal{X}$ are equivalent, where $\mathcal{X}_n^\sim$ is the order continuous dual of $\mathcal{X}$. We also provide some application to proper quasiconvex law-invariant functionals with the Fatou property.

Suggested Citation

  • Made Tantrawan & Denny H. Leung, 2018. "On closedness of law-invariant convex sets in rearrangement invariant spaces," Papers 1810.10374, arXiv.org, revised Dec 2019.
    • Handle: RePEc:arx:papers:1810.10374
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    References listed on IDEAS

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    1. Niushan Gao & Denny Leung & Cosimo Munari & Foivos Xanthos, 2018. "Fatou property, representations, and extensions of law-invariant risk measures on general Orlicz spaces," Finance and Stochastics, Springer, vol. 22(2), pages 395-415, April.
    2. Keita Owari, 2013. "Maximum Lebesgue Extension of Monotone Convex Functions," CARF F-Series CARF-F-315, 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. repec:dau:papers:123456789/342 is not listed on IDEAS
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