Robust quasi-convex risk measures and applications
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911526657458176 |
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| author | Centrone, Francesca Hitaj, Asmerilda Mastrogiacomo, Elisa Gianin, Emanuela Rosazza |
| author_facet | Centrone, Francesca Hitaj, Asmerilda Mastrogiacomo, Elisa Gianin, Emanuela Rosazza |
| contents | This paper develops a unified framework for the robustification of risk measures beyond the classical convex and cash-additive setting. We consider general risk measures on Lp spaces and construct their robust counterparts through families of uncertainty sets that capture ambiguity. Two complementary mechanisms generate robust quasi-convex measures: in the first, quasi-convexity is inherited from the initial risk measure under convex uncertainty sets; in the second it comes from the quasi-convex (or c-quasi-convex) structure of the uncertainty sets themselves. Building on Cerreia-Vioglio et al. (2011); Frittelli and Maggis (2011), we derive dual (penalty-type) representations for robust quasi-convex and cash-subadditive risk measures, showing that the classical convex cash-additive case arises as a special instance. We further analyze acceptance families and capital allocation rules under robustification, highlighting how ambiguity affects acceptability and the distribution of capital. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17954 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robust quasi-convex risk measures and applications Centrone, Francesca Hitaj, Asmerilda Mastrogiacomo, Elisa Gianin, Emanuela Rosazza Risk Management Probability Mathematical Finance This paper develops a unified framework for the robustification of risk measures beyond the classical convex and cash-additive setting. We consider general risk measures on Lp spaces and construct their robust counterparts through families of uncertainty sets that capture ambiguity. Two complementary mechanisms generate robust quasi-convex measures: in the first, quasi-convexity is inherited from the initial risk measure under convex uncertainty sets; in the second it comes from the quasi-convex (or c-quasi-convex) structure of the uncertainty sets themselves. Building on Cerreia-Vioglio et al. (2011); Frittelli and Maggis (2011), we derive dual (penalty-type) representations for robust quasi-convex and cash-subadditive risk measures, showing that the classical convex cash-additive case arises as a special instance. We further analyze acceptance families and capital allocation rules under robustification, highlighting how ambiguity affects acceptability and the distribution of capital. |
| title | Robust quasi-convex risk measures and applications |
| topic | Risk Management Probability Mathematical Finance |
| url | https://arxiv.org/abs/2603.17954 |