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Star-shaped acceptability indexes

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  • Righi, Marcelo Brutti

Abstract

We propose the star-shaped acceptability indexes as generalizations of both the approaches of Cherny and Madan (2009) and Rosazza Gianin and Sgarra (2013) in the same vein as star-shaped risk measures generalize both the classes of coherent and convex risk measures in Castagnoli et al. (2022). We characterize acceptability indexes through star-shaped risk measures and star-shaped acceptance sets as the minimum of a family of quasi-concave acceptability indexes. Further, we introduce concrete examples under our approach linked to Value at Risk, risk-adjusted reward on capital, reward-based gain-loss ratio, and monotone reward-deviation ratio.

Suggested Citation

  • Righi, Marcelo Brutti, 2024. "Star-shaped acceptability indexes," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 170-181.
    • Handle: RePEc:eee:insuma:v:117:y:2024:i:c:p:170-181
    DOI: 10.1016/j.insmatheco.2024.05.002
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    Cited by:

    1. Marcin Pitera & Mikl'os R'asonyi, 2023. "Utility-based acceptability indices," Papers 2310.02014, arXiv.org.
    2. Moresco, Marlon Ruoso & Righi, Marcelo Brutti, 2022. "On the link between monetary and star-shaped risk measures," Statistics & Probability Letters, Elsevier, vol. 184(C).

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    More about this item

    Keywords

    Star-shaped acceptability indexes; Star-shaped risk measures; Performance measures; Risk adjusted return on capital; Gain-loss ratio;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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