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Risk Measures’ Duality on Ordered Linear Spaces

Author

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  • Christos E. Kountzakis

    (Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, 83200 Karlovassi, Samos, Greece)

  • Damiano Rossello

    (Department of Economics, University of Catania, Corso Italia, 55, I-95129 Catania, Italy)

Abstract

The aim of this paper is to provide a dual representation of convex and coherent risk measures in partially ordered linear spaces with respect to the algebraic dual space. An algebraic robust representation is deduced by weak separation of convex sets by functionals, which are assumed to be only linear; thus, our framework does not require any topological structure of the underlying spaces, and our robust representations are found without any continuity requirement for the risk measures. We also use such extensions to the representation of acceptability indices.

Suggested Citation

  • Christos E. Kountzakis & Damiano Rossello, 2024. "Risk Measures’ Duality on Ordered Linear Spaces," Mathematics, MDPI, vol. 12(8), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1165-:d:1374828
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    References listed on IDEAS

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