Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.19648 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914189779402752 |
|---|---|
| author | Zawisza, Dariusz |
| author_facet | Zawisza, Dariusz |
| contents | We consider a finite-time stochastic drift control problem with the assumption that the control is bounded and the system is controlled until the state process leaves the half-line. Assuming general conditions, it is proved that the resulting parabolic Hamilton-Jacobi-Bellman equation has a classical solution. In fact, we consider an even more general family of semilinear equations, which might be helpful in solving other control or game problems. Not only is the existence result proved, but also a recursive procedure for finding a solution resulting from a fixed-point argument is provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19648 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic exit-time control on the half-line over a finite horizon Zawisza, Dariusz Optimization and Control Analysis of PDEs Probability We consider a finite-time stochastic drift control problem with the assumption that the control is bounded and the system is controlled until the state process leaves the half-line. Assuming general conditions, it is proved that the resulting parabolic Hamilton-Jacobi-Bellman equation has a classical solution. In fact, we consider an even more general family of semilinear equations, which might be helpful in solving other control or game problems. Not only is the existence result proved, but also a recursive procedure for finding a solution resulting from a fixed-point argument is provided. |
| title | Stochastic exit-time control on the half-line over a finite horizon |
| topic | Optimization and Control Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2503.19648 |