Star-shaped acceptability indexes

Marcelo Righi ()

Insurance: Mathematics and Economics, 2024, vol. 117, issue C, 170-181

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.

Keywords: Star-shaped acceptability indexes; Star-shaped risk measures; Performance measures; Risk adjusted return on capital; Gain-loss ratio (search for similar items in EconPapers)
JEL-codes: C61 G11 G22 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:117:y:2024:i:c:p:170-181

DOI: 10.1016/j.insmatheco.2024.05.002

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