The one-shot problem: Solution to an open question of finite-fuel singular control with discretionary stopping
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_ | 1866912108282642432 |
|---|---|
| author | Moriarty, John Rodosthenous, Neofytos |
| author_facet | Moriarty, John Rodosthenous, Neofytos |
| contents | We introduce a novel 'one-shot' solution technique resolving an open problem (Karatzas et al., Finite-fuel singular control with discretionary stopping, Stochastics 71:1-2 (2000)). Unexpectedly given the convexity of the latter problem, its waiting region is not necessarily connected. Along a typical sample path, the state process may even spend positive time in both of its connected components. The analysis reveals more generally that when fuel is limited, contrary to intuition, the solution without fuel is not necessarily indicative of the solution for small amounts of fuel. To resolve this, we recommend solving the `one-shot' problem, which is one of optimal stopping, prior to employing the usual `guess and verify' solution approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04301 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The one-shot problem: Solution to an open question of finite-fuel singular control with discretionary stopping Moriarty, John Rodosthenous, Neofytos Optimization and Control 93E20, 60G40 (Primary) 60J65 (Secondary) We introduce a novel 'one-shot' solution technique resolving an open problem (Karatzas et al., Finite-fuel singular control with discretionary stopping, Stochastics 71:1-2 (2000)). Unexpectedly given the convexity of the latter problem, its waiting region is not necessarily connected. Along a typical sample path, the state process may even spend positive time in both of its connected components. The analysis reveals more generally that when fuel is limited, contrary to intuition, the solution without fuel is not necessarily indicative of the solution for small amounts of fuel. To resolve this, we recommend solving the `one-shot' problem, which is one of optimal stopping, prior to employing the usual `guess and verify' solution approach. |
| title | The one-shot problem: Solution to an open question of finite-fuel singular control with discretionary stopping |
| topic | Optimization and Control 93E20, 60G40 (Primary) 60J65 (Secondary) |
| url | https://arxiv.org/abs/2411.04301 |