Long-Term Average Impulse Control with Mean Field Interactions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912872514191360 |
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| author | Helmes, K. L. Stockbridge, R. H. Zhu, C. |
| author_facet | Helmes, K. L. Stockbridge, R. H. Zhu, C. |
| contents | This paper analyzes and explicitly solves a class of long-term average impulse control problems with a specific mean-field interaction. The underlying process is a general one-dimensional diffusion with appropriate boundary behavior. The model is motivated by applications such as the optimal long-term management of renewable resources and financial portfolio management. Each individual agent seeks to maximize her long-term average reward, which consists of a running reward and income from discrete impulses, where the unit intervention price depends on the market through a stationary supply rate, the specific mean field variable to be considered. In a competitive market setting, we establish the existence of and explicitly characterize an equilibrium strategy within a large class of policies under mild conditions. Additionally, we formulate and solve the mean field control problem, in which agents cooperate with each other, aiming to realize a common maximal long-term average profit. To illustrate the theoretical results, we examine a stochastic logistic growth model and a population growth model in a stochastic environment with impulse control. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_11345 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Long-Term Average Impulse Control with Mean Field Interactions Helmes, K. L. Stockbridge, R. H. Zhu, C. Optimization and Control Probability 91A16, 91A15, 93E20, 60H30, 60J60, 91G80 This paper analyzes and explicitly solves a class of long-term average impulse control problems with a specific mean-field interaction. The underlying process is a general one-dimensional diffusion with appropriate boundary behavior. The model is motivated by applications such as the optimal long-term management of renewable resources and financial portfolio management. Each individual agent seeks to maximize her long-term average reward, which consists of a running reward and income from discrete impulses, where the unit intervention price depends on the market through a stationary supply rate, the specific mean field variable to be considered. In a competitive market setting, we establish the existence of and explicitly characterize an equilibrium strategy within a large class of policies under mild conditions. Additionally, we formulate and solve the mean field control problem, in which agents cooperate with each other, aiming to realize a common maximal long-term average profit. To illustrate the theoretical results, we examine a stochastic logistic growth model and a population growth model in a stochastic environment with impulse control. |
| title | Long-Term Average Impulse Control with Mean Field Interactions |
| topic | Optimization and Control Probability 91A16, 91A15, 93E20, 60H30, 60J60, 91G80 |
| url | https://arxiv.org/abs/2505.11345 |