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The strong Fatou property of risk measures

Author

Listed:
  • Chen Shengzhong

    (Department of Mathematics, Ryerson University,Toronto, Canada)

  • Gao Niushan

    (Department of Mathematics, Ryerson University,Toronto, Canada)

  • Xanthos Foivos

    (Department of Mathematics, Ryerson University,Toronto, Canada)

Abstract

In this paper, we explore several Fatou-type properties of risk measures. The paper continues to reveal that the strong Fatou property,whichwas introduced in [19], seems to be most suitable to ensure nice dual representations of risk measures. Our main result asserts that every quasiconvex law-invariant functional on a rearrangement invariant space X with the strong Fatou property is (X, L1) lower semicontinuous and that the converse is true on a wide range of rearrangement invariant spaces. We also study inf-convolutions of law-invariant or surplus-invariant risk measures that preserve the (strong) Fatou property.

Suggested Citation

  • Chen Shengzhong & Gao Niushan & Xanthos Foivos, 2018. "The strong Fatou property of risk measures," Dependence Modeling, De Gruyter, vol. 6(1), pages 183-196, October.
    • Handle: RePEc:vrs:demode:v:6:y:2018:i:1:p:183-196:n:12
    DOI: 10.1515/demo-2018-0012
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    References listed on IDEAS

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    Cited by:

    1. Felix-Benedikt Liebrich & Gregor Svindland, 2018. "Risk sharing for capital requirements with multidimensional security markets," Papers 1809.10015, arXiv.org.

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