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Fatou property, representations, and extensions of law-invariant risk measures on general Orlicz spaces

Author

Listed:
  • Niushan Gao

    (University of Lethbridge)

  • Denny Leung

    (National University of Singapore)

  • Cosimo Munari

    (University of Zurich)

  • Foivos Xanthos

    (Ryerson University)

Abstract

We provide a variety of results for quasiconvex, law-invariant functionals defined on a general Orlicz space, which extend well-known results from the setting of bounded random variables. First, we show that Delbaen’s representation of convex functionals with the Fatou property, which fails in a general Orlicz space, can always be achieved under the assumption of law-invariance. Second, we identify the class of Orlicz spaces where the characterization of the Fatou property in terms of norm-lower semicontinuity by Jouini, Schachermayer and Touzi continues to hold. Third, we extend Kusuoka’s representation to a general Orlicz space. Finally, we prove a version of the extension result by Filipović and Svindland by replacing norm-lower semicontinuity with the (generally non-equivalent) Fatou property. Our results have natural applications to the theory of risk measures.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:finsto:v:22:y:2018:i:2:d:10.1007_s00780-018-0357-7
    DOI: 10.1007/s00780-018-0357-7
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    References listed on IDEAS

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    More about this item

    Keywords

    Risk measures; Law-invariance; Fatou property; Dual representations; Conditional expectations; Orlicz spaces;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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