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A quantitative comparison of risk measures

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  • Alois Pichler

    (Technische Universität Chemnitz, Fakultät für Mathematik)

Abstract

The choice of a risk measure reflects a subjective preference of the decision maker in many managerial or real world economic problem formulations. To assess the impact of personal preferences it is thus of interest to have comparisons with other risk measures at hand. This paper develops a framework for comparing different risk measures. We establish a one-to-one relationship between norms and risk measures, that is, we associate a norm with a risk measure and conversely, we use norms to recover a genuine risk measure. The methods allow tight comparisons of risk measures and tight lower and upper bounds for risk measures are made available whenever possible. In this way we present a general framework for comparing risk measures with applications in numerous directions.

Suggested Citation

  • Alois Pichler, 2017. "A quantitative comparison of risk measures," Annals of Operations Research, Springer, vol. 254(1), pages 251-275, July.
    • Handle: RePEc:spr:annopr:v:254:y:2017:i:1:d:10.1007_s10479-017-2397-3
    DOI: 10.1007/s10479-017-2397-3
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    Cited by:

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    2. Alois Pichler, 2024. "Higher order measures of risk and stochastic dominance," Papers 2402.15387, arXiv.org.
    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. Yuliya Mishura & Kostiantyn Ralchenko & Petro Zelenko & Volodymyr Zubchenko, 2024. "Properties of the entropic risk measure EVaR in relation to selected distributions," Papers 2403.01468, arXiv.org.
    5. Behnam Malakooti & Mohamed Komaki & Camelia Al-Najjar, 2021. "Basic Geometric Dispersion Theory of Decision Making Under Risk: Asymmetric Risk Relativity, New Predictions of Empirical Behaviors, and Risk Triad," Decision Analysis, INFORMS, vol. 18(1), pages 41-77, March.
    6. Gao, Niushan & Munari, Cosimo & Xanthos, Foivos, 2020. "Stability properties of Haezendonck–Goovaerts premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 94-99.
    7. Sjur Didrik Flåm, 2019. "Blocks of coordinates, stochastic programming, and markets," Computational Management Science, Springer, vol. 16(1), pages 3-16, February.
    8. Amir Ahmadi-Javid & Malihe Fallah-Tafti, 2017. "Portfolio Optimization with Entropic Value-at-Risk," Papers 1708.05713, arXiv.org.
    9. Tom Erik Sønsteng Henriksen & Alois Pichler & Sjur Westgaard & Stein Frydenberg, 2019. "Can commodities dominate stock and bond portfolios?," Annals of Operations Research, Springer, vol. 282(1), pages 155-177, November.
    10. Righi, Marcelo Brutti & Borenstein, Denis, 2018. "A simulation comparison of risk measures for portfolio optimization," Finance Research Letters, Elsevier, vol. 24(C), pages 105-112.
    11. Danny Samson & Pat Foley & Heng Soon Gan & Marianne Gloet, 2018. "Multi-stakeholder decision theory," Annals of Operations Research, Springer, vol. 268(1), pages 357-386, September.

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