A General Theory of Risk Sharing
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910038387326976 |
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| author | Melnikov, Vasily |
| author_facet | Melnikov, Vasily |
| contents | We introduce a new paradigm for risk sharing that generalizes earlier models based on discrete agents and extends them to allow for sharing risk within a continuum of agents. Agents are represented by points of a measure space and have potentially heterogeneous risk preferences modeled by risk measures on a separable probability space. We derive the dual representation of the value function using a Strassen-type theorem for the weak-star topology and provide a characterization of the acceptance set using Aumann integration. These results are illustrated by explicit formulas when risk preferences are within the family of entropic and expected shortfall risk measures, and applications to Pareto efficiency in large markets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19276 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A General Theory of Risk Sharing Melnikov, Vasily Risk Management Theoretical Economics Mathematical Finance 91B05, 91G70 We introduce a new paradigm for risk sharing that generalizes earlier models based on discrete agents and extends them to allow for sharing risk within a continuum of agents. Agents are represented by points of a measure space and have potentially heterogeneous risk preferences modeled by risk measures on a separable probability space. We derive the dual representation of the value function using a Strassen-type theorem for the weak-star topology and provide a characterization of the acceptance set using Aumann integration. These results are illustrated by explicit formulas when risk preferences are within the family of entropic and expected shortfall risk measures, and applications to Pareto efficiency in large markets. |
| title | A General Theory of Risk Sharing |
| topic | Risk Management Theoretical Economics Mathematical Finance 91B05, 91G70 |
| url | https://arxiv.org/abs/2505.19276 |