Optimal withdrawals in a general diffusion model with control rates subject to a state-dependent upper bound
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_ | 1866913394033950720 |
|---|---|
| author | Guérin, Hélène Mata, Dante Renaud, Jean-François Roch, Alexandre |
| author_facet | Guérin, Hélène Mata, Dante Renaud, Jean-François Roch, Alexandre |
| contents | We consider a classical stochastic control problem in which a diffusion process is controlled by a withdrawal process up to a termination time. The objective is to maximize the expected discounted value of the withdrawals until the first-passage time below level zero. In this work, we are considering absolutely continuous control strategies in a general diffusion model. Our main contribution is a solution to the control problem under study, which is achieved by using a probabilistic guess-and-verify approach. We prove that the optimal strategy belongs to the family of bang-bang strategies, i.e. strategies in which, above an optimal barrier level, we withdraw at the highest-allowed rate, while no withdrawals are made below this barrier. Some nontrivial examples are studied numerically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12067 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal withdrawals in a general diffusion model with control rates subject to a state-dependent upper bound Guérin, Hélène Mata, Dante Renaud, Jean-François Roch, Alexandre Probability Optimization and Control 93E20, 60J60, 60J70 We consider a classical stochastic control problem in which a diffusion process is controlled by a withdrawal process up to a termination time. The objective is to maximize the expected discounted value of the withdrawals until the first-passage time below level zero. In this work, we are considering absolutely continuous control strategies in a general diffusion model. Our main contribution is a solution to the control problem under study, which is achieved by using a probabilistic guess-and-verify approach. We prove that the optimal strategy belongs to the family of bang-bang strategies, i.e. strategies in which, above an optimal barrier level, we withdraw at the highest-allowed rate, while no withdrawals are made below this barrier. Some nontrivial examples are studied numerically. |
| title | Optimal withdrawals in a general diffusion model with control rates subject to a state-dependent upper bound |
| topic | Probability Optimization and Control 93E20, 60J60, 60J70 |
| url | https://arxiv.org/abs/2406.12067 |