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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. Denuit, Michel & Dhaene, Jan, 2012. "Convex order and comonotonic conditional mean risk sharing," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 265-270.
    2. 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.
    3. 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.
    4. Andreas Haier & Ilya Molchanov, 2019. "Multivariate risk measures in the non-convex setting," Papers 1902.00766, arXiv.org, revised Sep 2019.
    5. Massoomeh Rahsepar & Foivos Xanthos, 2020. "On the extension property of dilatation monotone risk measures," Papers 2002.11865, arXiv.org.
    6. Leitner, Johannes, 2005. "Dilatation monotonous Choquet integrals," Journal of Mathematical Economics, Elsevier, vol. 41(8), pages 994-1006, December.
    7. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2015. "Shortfall Deviation Risk: An alternative to risk measurement," Papers 1501.02007, arXiv.org, revised May 2016.
    8. 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.
    9. 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.

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