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A composition between risk and deviation measures

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  • Marcelo Brutti Righi

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.

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  • Marcelo Brutti Righi, 2015. "A composition between risk and deviation measures," Papers 1511.06943, arXiv.org, revised May 2018.
    • Handle: RePEc:arx:papers:1511.06943
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    12. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2015. "Shortfall Deviation Risk: An alternative to risk measurement," Papers 1501.02007, arXiv.org, revised May 2016.
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    17. repec:dau:papers:123456789/342 is not listed on IDEAS
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    Cited by:

    1. Marcelo Brutti Righi, 2018. "A theory for combinations of risk measures," Papers 1807.01977, arXiv.org, revised May 2023.
    2. Wentao Hu & Cuixia Chen & Yufeng Shi & Ze Chen, 2022. "A Tail Measure With Variable Risk Tolerance: Application in Dynamic Portfolio Insurance Strategy," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 831-874, June.
    3. Mohammed Berkhouch & Fernanda Maria Müller & Ghizlane Lakhnati & Marcelo Brutti Righi, 2022. "Deviation-Based Model Risk Measures," Computational Economics, Springer;Society for Computational Economics, vol. 59(2), pages 527-547, February.
    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.

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