A mean-field version of Bank-El Karoui's representation of stochastic processes
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866918091193057280 |
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| author | He, Xihao Tan, Xiaolu Zou, Jun |
| author_facet | He, Xihao Tan, Xiaolu Zou, Jun |
| contents | We study a mean-field version of Bank-El Karoui's representation theorem of stochastic processes. Under different technical conditions, we establish some existence and uniqueness results. As motivation and first applications, our mean-field representation results provide a unified approach to study different Mean-Field Games (MFGs) in the setting with common noise and multiple populations, including the MFG of timing, the MFG with singular control, etc. As a crucial technical step, we provide a stability result on the classical Bank-El Karoui's representation theorem, which has its own interests and other applications, such as in deriving stability results of the optimizers (in the strong sense) for a class of optimal stopping problems and singular control problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_03300 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A mean-field version of Bank-El Karoui's representation of stochastic processes He, Xihao Tan, Xiaolu Zou, Jun Probability 60G40, 93E20, 60G07, 93E15 We study a mean-field version of Bank-El Karoui's representation theorem of stochastic processes. Under different technical conditions, we establish some existence and uniqueness results. As motivation and first applications, our mean-field representation results provide a unified approach to study different Mean-Field Games (MFGs) in the setting with common noise and multiple populations, including the MFG of timing, the MFG with singular control, etc. As a crucial technical step, we provide a stability result on the classical Bank-El Karoui's representation theorem, which has its own interests and other applications, such as in deriving stability results of the optimizers (in the strong sense) for a class of optimal stopping problems and singular control problems. |
| title | A mean-field version of Bank-El Karoui's representation of stochastic processes |
| topic | Probability 60G40, 93E20, 60G07, 93E15 |
| url | https://arxiv.org/abs/2302.03300 |