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Model Spaces for Risk Measures

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  • Felix-Benedikt Liebrich
  • Gregor Svindland

Abstract

We show how risk measures originally defined in a model free framework in terms of acceptance sets and reference assets imply a meaningful underlying probability structure. Hereafter we construct a maximal domain of definition of the risk measure respecting the underlying ambiguity profile. We particularly emphasise liquidity effects and discuss the correspondence between properties of the risk measure and the structure of this domain as well as subdifferentiability properties. Keywords: Model free risk assessment, extension of risk measures, continuity properties of risk measures, subgradients.

Suggested Citation

  • Felix-Benedikt Liebrich & Gregor Svindland, 2017. "Model Spaces for Risk Measures," Papers 1703.01137, arXiv.org, revised Nov 2017.
    • Handle: RePEc:arx:papers:1703.01137
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Arai, Takuji & Asano, Takao & Nishide, Katsumasa, 2019. "Optimal initial capital induced by the optimized certainty equivalent," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 115-125.
    2. Laudagé, Christian & Sass, Jörn & Wenzel, Jörg, 2022. "Combining multi-asset and intrinsic risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 254-269.
    3. Chen Shengzhong & Gao Niushan & Xanthos Foivos, 2018. "The strong Fatou property of risk measures," Dependence Modeling, De Gruyter, vol. 6(1), pages 183-196, October.
    4. Muqiao Huang & Ruodu Wang, 2024. "Coherent risk measures and uniform integrability," Papers 2404.03783, arXiv.org, revised Oct 2024.
    5. Felix-Benedikt Liebrich & Max Nendel, 2020. "Separability vs. robustness of Orlicz spaces: financial and economic perspectives," Papers 2009.09007, arXiv.org, revised May 2021.
    6. Shengzhong Chen & Niushan Gao & Foivos Xanthos, 2018. "The strong Fatou property of risk measures," Papers 1805.05259, arXiv.org.
    7. Fabio Bellini & Pablo Koch-Medina & Cosimo Munari & Gregor Svindland, 2018. "Law-invariant functionals on general spaces of random variables," Papers 1808.00821, arXiv.org, revised Jan 2021.
    8. Felix-Benedikt Liebrich & Gregor Svindland, 2019. "Risk sharing for capital requirements with multidimensional security markets," Finance and Stochastics, Springer, vol. 23(4), pages 925-973, October.
    9. Niushan Gao & Cosimo Munari, 2020. "Surplus-Invariant Risk Measures," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1342-1370, November.
    10. Felix-Benedikt Liebrich & Gregor Svindland, 2018. "Risk sharing for capital requirements with multidimensional security markets," Papers 1809.10015, arXiv.org.
    11. Marlon Moresco & Marcelo Righi & Eduardo Horta, 2020. "Minkowski gauges and deviation measures," Papers 2007.01414, arXiv.org, revised Jul 2021.
    12. Sascha Desmettre & Christian Laudagé & Jörn Sass, 2020. "Good-Deal Bounds for Option Prices under Value-at-Risk and Expected Shortfall Constraints," Risks, MDPI, vol. 8(4), pages 1-22, October.

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    Keywords

    model free risk assessment; extension of risk measures; continuity properties of risk measures; subgradients.;
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