On optimal tracking portfolio in incomplete markets: The reinforcement learning approach
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912097492795392 |
|---|---|
| author | Bo, Lijun Huang, Yijie Yu, Xiang |
| author_facet | Bo, Lijun Huang, Yijie Yu, Xiang |
| contents | This paper studies an infinite horizon optimal tracking portfolio problem using capital injection in incomplete market models. The benchmark process is modelled by a geometric Brownian motion with zero drift driven by some unhedgeable risk. The relaxed tracking formulation is adopted where the fund account compensated by the injected capital needs to outperform the benchmark process at any time, and the goal is to minimize the cost of the discounted total capital injection. When model parameters are known, we formulate the equivalent auxiliary control problem with reflected state dynamics, for which the classical solution of the HJB equation with Neumann boundary condition is obtained explicitly. When model parameters are unknown, we introduce the exploratory formulation for the auxiliary control problem with entropy regularization and develop the continuous-time q-learning algorithm in models of reflected diffusion processes. In some illustrative numerical example, we show the satisfactory performance of the q-learning algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_14318 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On optimal tracking portfolio in incomplete markets: The reinforcement learning approach Bo, Lijun Huang, Yijie Yu, Xiang Portfolio Management Optimization and Control This paper studies an infinite horizon optimal tracking portfolio problem using capital injection in incomplete market models. The benchmark process is modelled by a geometric Brownian motion with zero drift driven by some unhedgeable risk. The relaxed tracking formulation is adopted where the fund account compensated by the injected capital needs to outperform the benchmark process at any time, and the goal is to minimize the cost of the discounted total capital injection. When model parameters are known, we formulate the equivalent auxiliary control problem with reflected state dynamics, for which the classical solution of the HJB equation with Neumann boundary condition is obtained explicitly. When model parameters are unknown, we introduce the exploratory formulation for the auxiliary control problem with entropy regularization and develop the continuous-time q-learning algorithm in models of reflected diffusion processes. In some illustrative numerical example, we show the satisfactory performance of the q-learning algorithm. |
| title | On optimal tracking portfolio in incomplete markets: The reinforcement learning approach |
| topic | Portfolio Management Optimization and Control |
| url | https://arxiv.org/abs/2311.14318 |