Maximum principle for stochastic optimal control problem under convex expectation
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_ | 1866911996001124352 |
|---|---|
| author | Li, Xiaojuan Hu, Mingshang |
| author_facet | Li, Xiaojuan Hu, Mingshang |
| contents | In this paper, we study a stochastic optimal control problem under a type of consistent convex expectation dominated by G-expectation. By the separation theorem for convex sets, we get the representation theorems for this convex expectation and conditional convex expectation. Based on these results, we obtain the variational equation for cost functional by weak convergence and discretization methods. Furthermore, we establish the maximum principle which is sufficient under usual convex assumptions. Finally, we study the linear quadratic control problem by using the obtained maximum principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10587 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximum principle for stochastic optimal control problem under convex expectation Li, Xiaojuan Hu, Mingshang Optimization and Control 93E20, 60H10, 35K15 In this paper, we study a stochastic optimal control problem under a type of consistent convex expectation dominated by G-expectation. By the separation theorem for convex sets, we get the representation theorems for this convex expectation and conditional convex expectation. Based on these results, we obtain the variational equation for cost functional by weak convergence and discretization methods. Furthermore, we establish the maximum principle which is sufficient under usual convex assumptions. Finally, we study the linear quadratic control problem by using the obtained maximum principle. |
| title | Maximum principle for stochastic optimal control problem under convex expectation |
| topic | Optimization and Control 93E20, 60H10, 35K15 |
| url | https://arxiv.org/abs/2408.10587 |