Generalized Orlicz premia
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909686531358720 |
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| author | Aygün, Mücahit Bellini, Fabio Laeven, Roger J. A. |
| author_facet | Aygün, Mücahit Bellini, Fabio Laeven, Roger J. A. |
| contents | We introduce a generalized version of Orlicz premia, based on possibly non-convex loss functions. We show that this generalized definition covers a variety of relevant examples, such as the geometric mean and the expectiles, while at the same time retaining a number of relevant properties. We establish that cash-additivity leads to $L^p$-quantiles, extending a classical result on 'collapse to the mean' for convex Orlicz premia.
We then focus on the geometrically convex case, discussing the dual representation of generalized Orlicz premia and comparing it with a multiplicative form of the standard dual representation for the convex case. Finally, we show that generalized Orlicz premia arise naturally as the only elicitable, positively homogeneous, monotone and normalized functionals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09181 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Orlicz premia Aygün, Mücahit Bellini, Fabio Laeven, Roger J. A. Risk Management Probability Statistics Theory Mathematical Finance We introduce a generalized version of Orlicz premia, based on possibly non-convex loss functions. We show that this generalized definition covers a variety of relevant examples, such as the geometric mean and the expectiles, while at the same time retaining a number of relevant properties. We establish that cash-additivity leads to $L^p$-quantiles, extending a classical result on 'collapse to the mean' for convex Orlicz premia. We then focus on the geometrically convex case, discussing the dual representation of generalized Orlicz premia and comparing it with a multiplicative form of the standard dual representation for the convex case. Finally, we show that generalized Orlicz premia arise naturally as the only elicitable, positively homogeneous, monotone and normalized functionals. |
| title | Generalized Orlicz premia |
| topic | Risk Management Probability Statistics Theory Mathematical Finance |
| url | https://arxiv.org/abs/2507.09181 |