Bipolar Theorems for Sets of Non-negative Random Variables
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866917512250130432 |
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| author | Langner, Johannes Svindland, Gregor |
| author_facet | Langner, Johannes Svindland, Gregor |
| contents | This paper assumes a robust, in general not dominated, probabilistic framework and provides necessary and sufficient conditions for a bipolar representation of subsets of the set of all quasi-sure equivalence classes of non-negative random variables, without any further conditions on the underlying measure space. This generalizes and unifies existing bipolar theorems proved under stronger assumptions on the robust framework. Applications are in areas of robust financial modeling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_14259 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bipolar Theorems for Sets of Non-negative Random Variables Langner, Johannes Svindland, Gregor Probability Functional Analysis Mathematical Finance 46A20, 46E30, 46N10, 46N30, 60B11, 91G80 This paper assumes a robust, in general not dominated, probabilistic framework and provides necessary and sufficient conditions for a bipolar representation of subsets of the set of all quasi-sure equivalence classes of non-negative random variables, without any further conditions on the underlying measure space. This generalizes and unifies existing bipolar theorems proved under stronger assumptions on the robust framework. Applications are in areas of robust financial modeling. |
| title | Bipolar Theorems for Sets of Non-negative Random Variables |
| topic | Probability Functional Analysis Mathematical Finance 46A20, 46E30, 46N10, 46N30, 60B11, 91G80 |
| url | https://arxiv.org/abs/2212.14259 |