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Monetary Risk Functionals on Orlicz Spaces Produced by Set-Valued Risk Maps and Random Measures

In: Mathematical and Statistical Methods for Actuarial Sciences and Finance

Author

Listed:
  • Dimitrios G. Konstantinides

    (University of the Aegean, Department of Mathematics)

  • Christos E. Kountzakis

    (University of the Aegean, Department of Mathematics)

Abstract

In this article we study the construction of coherent or convex risk functionals defined either on an Orlicz heart, either on an Orlicz space, with respect to a Young loss function. The Orlicz heart is taken as a subset of $L^{0}(\varOmega, \mathcal{F}, \mu)$ endowed with the pointwise partial ordering. We define set-valued risk maps related to this partial ordering. We also derive monetary risk functionals both by the class of coherent set-valued risk maps defined on them. We also use random measures related to heavy-tailed distributions in order to define monetary risk functionals on Orlicz spaces, whose properties are also compared to the previous ones.

Suggested Citation

  • Dimitrios G. Konstantinides & Christos E. Kountzakis, 2014. "Monetary Risk Functionals on Orlicz Spaces Produced by Set-Valued Risk Maps and Random Measures," Springer Books, in: Cira Perna & Marilena Sibillo (ed.), Mathematical and Statistical Methods for Actuarial Sciences and Finance, edition 127, pages 125-128, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-05014-0_29
    DOI: 10.1007/978-3-319-05014-0_29
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