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Positivity

, Volume 18, Issue 3, pp 619–639 | Cite as

Representations of set-valued risk measures defined on the \(l\)-tensor product of Banach lattices

  • Coenraad C. A. LabuschagneEmail author
  • Theresa M. Offwood-Le Roux
Article

Abstract

We obtain a representation for set-valued risk measures which are defined on the completed \(l\)-tensor product \(E\widetilde{\otimes }_l G\) of Banach lattices \(E\) and \(G\). This representation extends known representations for set-valued risk measures defined on Bochner spaces \(L^p(\mathbb {P}, \mathbb {R}^d)\) of \(p\)-integrable functions with values in \(\mathbb {R}^d\).

Keywords

Orlicz space Orlicz heart Banach lattice Tensor product  Set-valued risk measure 

Mathematics Subject Classification (2010)

46A40 46B40 46E30 46E40 91B30 

Notes

Acknowledgments

This work is based on research supported by the National Research Foundation, the Mellon Postgraduate Mentoring Programme and DAAD.

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Coenraad C. A. Labuschagne
    • 1
    Email author
  • Theresa M. Offwood-Le Roux
    • 2
  1. 1.Department of Finance and Investment ManagementUniversity of JohannesburgJohannesburgSouth Africa
  2. 2.Standard BankRosebankSouth Africa

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