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Balayage Monotonous Risk Measures

Author

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  • JOHANNES LEITNER

    (Institute for Mathematical Methods in Economics, Financial and Actuarial Mathematics, Vienna University of Technology, Wiedner Hauptstraße 8-10/105, A-1040 Vienna, Austria)

Abstract

We consider coherent risk measures satisfying the Fatou property which are monotonous with respect to balayage or dilatation. An equivalent condition ensuring balayage-monotonicity is given and a representation result is derived.

Suggested Citation

  • Johannes Leitner, 2004. "Balayage Monotonous Risk Measures," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(07), pages 887-900.
    • Handle: RePEc:wsi:ijtafx:v:07:y:2004:i:07:n:s0219024904002724
    DOI: 10.1142/S0219024904002724
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    Citations

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    Cited by:

    1. Massoomeh Rahsepar & Foivos Xanthos, 2020. "On the extension property of dilatation monotone risk measures," Papers 2002.11865, arXiv.org.
    2. Denuit, Michel & Dhaene, Jan, 2012. "Convex order and comonotonic conditional mean risk sharing," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 265-270.
    3. Leitner, Johannes, 2005. "Dilatation monotonous Choquet integrals," Journal of Mathematical Economics, Elsevier, vol. 41(8), pages 994-1006, December.
    4. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2015. "Shortfall Deviation Risk: An alternative to risk measurement," Papers 1501.02007, arXiv.org, revised May 2016.
    5. Haier Andreas & Molchanov Ilya, 2019. "Multivariate risk measures in the non-convex setting," Statistics & Risk Modeling, De Gruyter, vol. 36(1-4), pages 25-35, December.
    6. Bauerle, Nicole & Muller, Alfred, 2006. "Stochastic orders and risk measures: Consistency and bounds," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 132-148, February.
    7. Martin Herdegen & Nazem Khan, 2022. "Mean‐ρ$\rho$ portfolio selection and ρ$\rho$‐arbitrage for coherent risk measures," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 226-272, January.
    8. Grigoriev Pavel G. & Leitner Johannes, 2006. "Dilatation monotone and comonotonic additive risk measures represented as Choquet integrals," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-18, July.
    9. Andreas Haier & Ilya Molchanov, 2019. "Multivariate risk measures in the non-convex setting," Papers 1902.00766, arXiv.org, revised Sep 2019.

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