On conditioning and consistency for nonlinear functionals
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866915318645915648 |
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| author | Berton, Edoardo Doldi, Alessandro Maggis, Marco |
| author_facet | Berton, Edoardo Doldi, Alessandro Maggis, Marco |
| contents | We consider a family of conditional nonlinear expectations defined on the space of bounded random variables and indexed by the class of all the sub-sigma-algebras of a given underlying sigma-algebra. We show that if this family satisfies a natural consistency property, then it collapses to a conditional certainty equivalent defined in terms of a state-dependent utility function. This result is obtained by embedding our problem in a decision theoretical framework and providing a new characterization of the Sure-Thing Principle. In particular we prove that this principle characterizes those preference relations which admit consistent backward conditional projections. We build our analysis on state-dependent preferences for a general state space as in Wakker and Zank (1999) and show that their numerical representation admits a continuous version of the state-dependent utility. In this way, we also answer positively to a conjecture posed in the aforementioned paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09054 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On conditioning and consistency for nonlinear functionals Berton, Edoardo Doldi, Alessandro Maggis, Marco Mathematical Finance Theoretical Economics 91B06, 91B08, 60A05 We consider a family of conditional nonlinear expectations defined on the space of bounded random variables and indexed by the class of all the sub-sigma-algebras of a given underlying sigma-algebra. We show that if this family satisfies a natural consistency property, then it collapses to a conditional certainty equivalent defined in terms of a state-dependent utility function. This result is obtained by embedding our problem in a decision theoretical framework and providing a new characterization of the Sure-Thing Principle. In particular we prove that this principle characterizes those preference relations which admit consistent backward conditional projections. We build our analysis on state-dependent preferences for a general state space as in Wakker and Zank (1999) and show that their numerical representation admits a continuous version of the state-dependent utility. In this way, we also answer positively to a conjecture posed in the aforementioned paper. |
| title | On conditioning and consistency for nonlinear functionals |
| topic | Mathematical Finance Theoretical Economics 91B06, 91B08, 60A05 |
| url | https://arxiv.org/abs/2401.09054 |