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Originalpublikation
Bellini, F.; Koch-Medina, P.; Munari, C.; Svindland, G.: Law-invariant functionals that collapse to the mean. In: Insurance: Mathematics and Economics 98 (2021), S. 83-91. DOI: https://doi.org/10.1016/j.insmatheco.2021.03.002
Version im Repositorium
Zum Zitieren der Version im Repositorium verwenden Sie bitte diesen DOI:
https://doi.org/10.15488/12274
| Zusammenfassung: | |
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We discuss when law-invariant convex functionals “collapse to the mean”. More precisely, we show that, in a large class of spaces of random variables and under mild semicontinuity assumptions, the expectation functional is, up to an affine transformation, the only law-invariant convex functional that is linear along the direction of a nonconstant random variable with nonzero expectation. This extends results obtained in the literature in a bounded setting and under additional assumptions on the functionals. We illustrate the implications of our general results for pricing rules and risk measures. © 2021 The Author(s)
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| Lizenzbestimmungen: | CC BY 4.0 Unported - https://creativecommons.org/licenses/by/4.0/ |
| Publikationstyp: | Article |
| Publikationsstatus: | publishedVersion |
| Erstveröffentlichung: | 2021 |
| Schlagwörter (englisch): | Affinity, Law invariance, Pricing rules, Risk measures, Translation invariance |
| Fachliche Zuordnung (DDC): | 330 | Wirtschaft, 510 | Mathematik |
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