A risk-sensitive ergodic singular stochastic control problem
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912584552153088 |
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| author | Gwee, Justin Zervos, Mihail |
| author_facet | Gwee, Justin Zervos, Mihail |
| contents | We consider a two-sided singular stochastic control problem with a risk-sensitive ergodic criterion. In particular, we consider a stochastic system whose uncontrolled dynamics are modelled by a linear diffusion. The control that can be applied to the system is modelled by an additive finite variation process. The objective of the control problem is to minimise a risk-sensitive long-term average criterion that penalises deviations of the controlled process from a given interval, as well as the expenditure of control effort. The stochastic control problem has been partly motivated by the problem faced by a central bank who wish to control the exchange rate between its domestic currency and a foreign currency so that this fluctuates within a suitable target zone. We derive the complete solution to the problem under general assumptions by deriving a C2 solution to its HJB equation. To this end, we use the solutions to a suitable family of Sturm-Liouville eigenvalue problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09835 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A risk-sensitive ergodic singular stochastic control problem Gwee, Justin Zervos, Mihail Optimization and Control Probability We consider a two-sided singular stochastic control problem with a risk-sensitive ergodic criterion. In particular, we consider a stochastic system whose uncontrolled dynamics are modelled by a linear diffusion. The control that can be applied to the system is modelled by an additive finite variation process. The objective of the control problem is to minimise a risk-sensitive long-term average criterion that penalises deviations of the controlled process from a given interval, as well as the expenditure of control effort. The stochastic control problem has been partly motivated by the problem faced by a central bank who wish to control the exchange rate between its domestic currency and a foreign currency so that this fluctuates within a suitable target zone. We derive the complete solution to the problem under general assumptions by deriving a C2 solution to its HJB equation. To this end, we use the solutions to a suitable family of Sturm-Liouville eigenvalue problems. |
| title | A risk-sensitive ergodic singular stochastic control problem |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2509.09835 |