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A theory for combinations of risk measures

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  • Marcelo Brutti Righi

Abstract

We study combinations of risk measures under no restrictive assumption on the set of alternatives. We develop and discuss results regarding the preservation of properties and acceptance sets for the combinations of risk measures. One of the main results is the representation of resulting risk measures from the properties of both alternative functionals and combination functions. We build on developing a dual representation for an arbitrary mixture of convex risk measures. In this case, we obtain a penalty that recalls the notion of inf-convolution under theoretical measure integration. We develop results related to this specific context. We also explore features of individual interest generated by our frameworks, such as the preservation of continuity properties and the representation of worst-case risk measures.

Suggested Citation

  • Marcelo Brutti Righi, 2018. "A theory for combinations of risk measures," Papers 1807.01977, arXiv.org, revised May 2023.
    • Handle: RePEc:arx:papers:1807.01977
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    Cited by:

    1. Ruodu Wang & Johanna F. Ziegel, 2018. "Scenario-based Risk Evaluation," Papers 1808.07339, arXiv.org, revised May 2021.
    2. Righi, Marcelo Brutti, 2024. "Star-shaped acceptability indexes," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 170-181.
    3. Marlon Moresco & Marcelo Righi & Eduardo Horta, 2020. "Minkowski gauges and deviation measures," Papers 2007.01414, arXiv.org, revised Jul 2021.
    4. Ruodu Wang & Johanna F. Ziegel, 2021. "Scenario-based risk evaluation," Finance and Stochastics, Springer, vol. 25(4), pages 725-756, October.
    5. Marcelo Righi, 2024. "Robust convex risk measures," Papers 2406.12999, arXiv.org, revised Oct 2024.

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