Optimal dividend payout with path-dependent drawdown constraint
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915711607111680 |
|---|---|
| author | Guan, Chonghu Fan, Jiacheng Xu, Zuo Quan |
| author_facet | Guan, Chonghu Fan, Jiacheng Xu, Zuo Quan |
| contents | This paper studies an optimal dividend problem with a drawdown constraint in a Brownian motion model, requiring the dividend payout rate to remain above a fixed proportion of its historical maximum. This leads to a path-dependent stochastic control problem, as the admissible control depends on its own past values. The associated Hamilton-Jacobi-Bellman (HJB) equation is a novel two-dimensional variational inequality with a gradient constraint, a type of problem previously only analyzed in the literature using viscosity solution techniques. In contrast, this paper employs delicate PDE methods to establish the existence of a strong solution. This stronger regularity allows us to explicitly characterize an optimal feedback control strategy, expressed in terms of two free boundaries and the running maximum surplus process. Furthermore, we derive key properties of the value function and the free boundaries, including boundedness and continuity. Numerical examples are provided to verify the theoretical results and to offer new financial insights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01668 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimal dividend payout with path-dependent drawdown constraint Guan, Chonghu Fan, Jiacheng Xu, Zuo Quan Mathematical Finance Optimization and Control Portfolio Management 35R35, 35Q93, 91G10, 91G30, 93E20 This paper studies an optimal dividend problem with a drawdown constraint in a Brownian motion model, requiring the dividend payout rate to remain above a fixed proportion of its historical maximum. This leads to a path-dependent stochastic control problem, as the admissible control depends on its own past values. The associated Hamilton-Jacobi-Bellman (HJB) equation is a novel two-dimensional variational inequality with a gradient constraint, a type of problem previously only analyzed in the literature using viscosity solution techniques. In contrast, this paper employs delicate PDE methods to establish the existence of a strong solution. This stronger regularity allows us to explicitly characterize an optimal feedback control strategy, expressed in terms of two free boundaries and the running maximum surplus process. Furthermore, we derive key properties of the value function and the free boundaries, including boundedness and continuity. Numerical examples are provided to verify the theoretical results and to offer new financial insights. |
| title | Optimal dividend payout with path-dependent drawdown constraint |
| topic | Mathematical Finance Optimization and Control Portfolio Management 35R35, 35Q93, 91G10, 91G30, 93E20 |
| url | https://arxiv.org/abs/2312.01668 |