Coordinated Mean-Field Control for Systemic Risk
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908693857042432 |
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| author | Yamanaka, Toshiaki |
| author_facet | Yamanaka, Toshiaki |
| contents | We develop a robust linear-quadratic mean-field control framework for systemic risk under model uncertainty, in which a central bank jointly optimizes interest rate policy and supervisory monitoring intensity against adversarial distortions. Our model features multiple policy instruments with interactive dynamics, implemented via a variance weight that depends on the policy rate, generating coupling effects absent in single-instrument models. We establish viscosity solutions for the associated HJB--Isaacs equation, prove uniqueness via comparison principles, and provide verification theorems. The linear-quadratic structure yields explicit feedback controls derived from a coupled Riccati system, preserving analytical tractability despite adversarial uncertainty. Simulations reveal distinct loss-of-control regimes driven by robustness-breakdown and control saturation, alongside a pronounced asymmetry in sensitivity between the mean and variance channels. These findings demonstrate the importance of instrument complementarity in systemic risk modeling and control. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04704 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coordinated Mean-Field Control for Systemic Risk Yamanaka, Toshiaki Optimization and Control Mathematical Finance We develop a robust linear-quadratic mean-field control framework for systemic risk under model uncertainty, in which a central bank jointly optimizes interest rate policy and supervisory monitoring intensity against adversarial distortions. Our model features multiple policy instruments with interactive dynamics, implemented via a variance weight that depends on the policy rate, generating coupling effects absent in single-instrument models. We establish viscosity solutions for the associated HJB--Isaacs equation, prove uniqueness via comparison principles, and provide verification theorems. The linear-quadratic structure yields explicit feedback controls derived from a coupled Riccati system, preserving analytical tractability despite adversarial uncertainty. Simulations reveal distinct loss-of-control regimes driven by robustness-breakdown and control saturation, alongside a pronounced asymmetry in sensitivity between the mean and variance channels. These findings demonstrate the importance of instrument complementarity in systemic risk modeling and control. |
| title | Coordinated Mean-Field Control for Systemic Risk |
| topic | Optimization and Control Mathematical Finance |
| url | https://arxiv.org/abs/2512.04704 |