Mean-field stochastic linear quadratic control problem with random coefficients
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913860214063104 |
|---|---|
| author | Xiong, Jie Xu, Wen |
| author_facet | Xiong, Jie Xu, Wen |
| contents | In this paper, we first prove that the mean-field stochastic linear quadratic (MFSLQ for short) control problem with random coefficients has a unique optimal control and derive a preliminary stochastic maximum principle to characterize this optimal control by an optimality system. However, because of the term of the form $\mathbb{E}[A_1(\cdot)^\top Y(\cdot)] $ in the adjoint equation, which cannot be represented in the form $\mathbb{E}[A_1(\cdot)^\top]\mathbb{E} [Y(\cdot)] $, we cannot solve this optimality system explicitly. To this end, we decompose the MFSLQ control problem into two problems without the mean-field terms, and one of them is a constrained problem. The constrained SLQ control problem is solved explicitly by an extended LaGrange multiplier method developed in this article. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04621 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mean-field stochastic linear quadratic control problem with random coefficients Xiong, Jie Xu, Wen Optimization and Control In this paper, we first prove that the mean-field stochastic linear quadratic (MFSLQ for short) control problem with random coefficients has a unique optimal control and derive a preliminary stochastic maximum principle to characterize this optimal control by an optimality system. However, because of the term of the form $\mathbb{E}[A_1(\cdot)^\top Y(\cdot)] $ in the adjoint equation, which cannot be represented in the form $\mathbb{E}[A_1(\cdot)^\top]\mathbb{E} [Y(\cdot)] $, we cannot solve this optimality system explicitly. To this end, we decompose the MFSLQ control problem into two problems without the mean-field terms, and one of them is a constrained problem. The constrained SLQ control problem is solved explicitly by an extended LaGrange multiplier method developed in this article. |
| title | Mean-field stochastic linear quadratic control problem with random coefficients |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2406.04621 |