Efficiency in Pure-Exchange Economies with Risk-Averse Monetary Utilities
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911987984760832 |
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| author | Ghossoub, Mario Zhu, Michael Boyuan |
| author_facet | Ghossoub, Mario Zhu, Michael Boyuan |
| contents | We study Pareto efficiency in a pure-exchange economy where agents' preferences are represented by risk-averse monetary utilities. These coincide with law-invariant monetary utilities, and they can be shown to correspond to the class of monotone, (quasi-)concave, Schur concave, and translation-invariant utility functionals. This covers a large class of utility functionals, including a variety of law-invariant robust utilities. We show that Pareto optima exist and are comonotone, and we provide a crisp characterization thereof in the case of law-invariant positively homogeneous monetary utilities. This characterization provides an easily implementable algorithm that fully determines the shape of Pareto-optimal allocations. In the special case of law-invariant comonotone-additive monetary utility functionals (concave Yaari-Dual utilities), we provide a closed-form characterization of Pareto optima. As an application, we examine risk-sharing markets where all agents evaluate risk through law-invariant coherent risk measures, a widely popular class of risk measures. In a numerical illustration, we characterize Pareto-optimal risk-sharing for some special types of coherent risk measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02712 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Efficiency in Pure-Exchange Economies with Risk-Averse Monetary Utilities Ghossoub, Mario Zhu, Michael Boyuan Mathematical Finance Theoretical Economics Risk Management We study Pareto efficiency in a pure-exchange economy where agents' preferences are represented by risk-averse monetary utilities. These coincide with law-invariant monetary utilities, and they can be shown to correspond to the class of monotone, (quasi-)concave, Schur concave, and translation-invariant utility functionals. This covers a large class of utility functionals, including a variety of law-invariant robust utilities. We show that Pareto optima exist and are comonotone, and we provide a crisp characterization thereof in the case of law-invariant positively homogeneous monetary utilities. This characterization provides an easily implementable algorithm that fully determines the shape of Pareto-optimal allocations. In the special case of law-invariant comonotone-additive monetary utility functionals (concave Yaari-Dual utilities), we provide a closed-form characterization of Pareto optima. As an application, we examine risk-sharing markets where all agents evaluate risk through law-invariant coherent risk measures, a widely popular class of risk measures. In a numerical illustration, we characterize Pareto-optimal risk-sharing for some special types of coherent risk measures. |
| title | Efficiency in Pure-Exchange Economies with Risk-Averse Monetary Utilities |
| topic | Mathematical Finance Theoretical Economics Risk Management |
| url | https://arxiv.org/abs/2406.02712 |