Star-shaped acceptability indexes
Risk Management
2024-05-28 v3
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.
Keywords
Cite
@article{arxiv.2110.08630,
title = {Star-shaped acceptability indexes},
author = {Marcelo Brutti Righi},
journal= {arXiv preprint arXiv:2110.08630},
year = {2024}
}