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Star-shaped acceptability indexes

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  • Marcelo Brutti Righi

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, star-shaped acceptance sets, and 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, monotone reward-deviation ratio, and robust acceptability indexes.

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  • Marcelo Brutti Righi, 2021. "Star-shaped acceptability indexes," Papers 2110.08630, arXiv.org, revised Jun 2022.
    • Handle: RePEc:arx:papers:2110.08630
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    References listed on IDEAS

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    Cited by:

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

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