Choquet integration with submodular function on measurable space with sigma-algebra generating chain
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912585641623552 |
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| author | Hattori, Tetsuya |
| author_facet | Hattori, Tetsuya |
| contents | Based on a study of a formula representing submodular set function as a supremum of measures dominated by the set function, we present a corresponding formula for a Choquet integration with respect to the set function, on a measurable space which has a chain of measurable set generating the sigma-algebra. As an application we reproduce a basic formula in mathematical finance on law invariant coherent risk measures. We also study a recursion relation of set functions for which the representation formula characterizes the fixed point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11033 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Choquet integration with submodular function on measurable space with sigma-algebra generating chain Hattori, Tetsuya Probability Based on a study of a formula representing submodular set function as a supremum of measures dominated by the set function, we present a corresponding formula for a Choquet integration with respect to the set function, on a measurable space which has a chain of measurable set generating the sigma-algebra. As an application we reproduce a basic formula in mathematical finance on law invariant coherent risk measures. We also study a recursion relation of set functions for which the representation formula characterizes the fixed point. |
| title | Choquet integration with submodular function on measurable space with sigma-algebra generating chain |
| topic | Probability |
| url | https://arxiv.org/abs/2509.11033 |