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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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    References listed on IDEAS

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    Cited by:

    1. Ahmadi-Javid, Amir & Fallah-Tafti, Malihe, 2019. "Portfolio optimization with entropic value-at-risk," European Journal of Operational Research, Elsevier, vol. 279(1), pages 225-241.
    2. Sjur Didrik Flåm, 2019. "Blocks of coordinates, stochastic programming, and markets," Computational Management Science, Springer, vol. 16(1), pages 3-16, February.
    3. 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.
    4. 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.
    5. 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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