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A composition between risk and deviation measures

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  • Marcelo Brutti Righi

    (Federal University of Rio Grande do Sul)

Abstract

The intuition of risk is based on two main concepts: loss and variability. In this paper, we present a composition of risk and deviation measures, which contemplate these two concepts. Based on the proposed Limitedness axiom, we prove that this resulting composition, based on properties of the two components, is a coherent risk measure. Similar results for the cases of convex and co-monotone risk measures are exposed. We also provide examples of known and new risk measures constructed under this framework in order to highlight the importance of our approach, especially the role of the Limitedness axiom.

Suggested Citation

  • Marcelo Brutti Righi, 2019. "A composition between risk and deviation measures," Annals of Operations Research, Springer, vol. 282(1), pages 299-313, November.
    • Handle: RePEc:spr:annopr:v:282:y:2019:i:1:d:10.1007_s10479-018-2913-0
    DOI: 10.1007/s10479-018-2913-0
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Felix-Benedikt Liebrich & Cosimo Munari, 2022. "Law-Invariant Functionals that Collapse to the Mean: Beyond Convexity," Mathematics and Financial Economics, Springer, volume 16, number 2, June.
    2. Gregor Dorfleitner, 2022. "On the use of the terminal-value approach in risk-value models," Annals of Operations Research, Springer, vol. 313(2), pages 877-897, June.
    3. Righi, Marcelo Brutti & Müller, Fernanda Maria & Moresco, Marlon Ruoso, 2020. "On a robust risk measurement approach for capital determination errors minimization," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 199-211.
    4. Müller, Fernanda Maria & Santos, Samuel Solgon & Righi, Marcelo Brutti, 2023. "A description of the COVID-19 outbreak role in financial risk forecasting," The North American Journal of Economics and Finance, Elsevier, vol. 66(C).
    5. Samuel Solgon Santos & Marlon Ruoso Moresco & Marcelo Brutti Righi & Eduardo de Oliveira Horta, 2023. "A note on the induction of comonotonic additive risk measures from acceptance sets," Papers 2307.04647, arXiv.org, revised Jul 2023.
    6. Nendel, Max & Riedel, Frank & Schmeck, Maren Diane, 2021. "A decomposition of general premium principles into risk and deviation," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 193-209.
    7. Alejandro Balbás & Beatriz Balbás & Raquel Balbás, 2022. "Pareto efficient buy and hold investment strategies under order book linked constraints," Annals of Operations Research, Springer, vol. 311(2), pages 945-965, April.
    8. Marcelo Brutti Righi & Marlon Ruoso Moresco, 2020. "Inf-convolution and optimal risk sharing with countable sets of risk measures," Papers 2003.05797, arXiv.org, revised Mar 2022.
    9. Marcelo Brutti Righi & Marlon Ruoso Moresco, 2022. "Star-Shaped deviations," Papers 2207.08613, arXiv.org.
    10. Hu, Taizhong & Chen, Ouxiang, 2020. "On a family of coherent measures of variability," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 173-182.
    11. Marcelo Brutti Righi & Fernanda Maria Muller & Marlon Ruoso Moresco, 2022. "A risk measurement approach from risk-averse stochastic optimization of score functions," Papers 2208.14809, arXiv.org, revised May 2023.
    12. Pablo Cristini Guedes & Fernanda Maria Müller & Marcelo Brutti Righi, 2023. "Risk measures-based cluster methods for finance," Risk Management, Palgrave Macmillan, vol. 25(1), pages 1-56, March.
    13. Marlon Moresco & Marcelo Righi & Eduardo Horta, 2020. "Minkowski gauges and deviation measures," Papers 2007.01414, arXiv.org, revised Jul 2021.
    14. Sant’Anna, Leonardo Riegel & Righi, Marcelo Brutti & Müller, Fernanda Maria & Guedes, Pablo Cristini, 2022. "Risk measure index tracking model," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 361-383.
    15. Marcelo Brutti Righi, 2021. "Star-shaped acceptability indexes," Papers 2110.08630, arXiv.org, revised Jun 2022.

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