A deep learning-driven iterative scheme for high-dimensional HJB equations in portfolio selection with exogenous and endogenous costs
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911134271930368 |
|---|---|
| author | Yan, Dong Zhang, Nanyi Guo, Junyi |
| author_facet | Yan, Dong Zhang, Nanyi Guo, Junyi |
| contents | In this paper, we first conduct a study of the portfolio selection problem, incorporating both exogenous (proportional) and endogenous (resulting from liquidity risk, characterized by a stochastic process) transaction costs through the utility-based approach. We also consider the intrinsic relationship between these two types of costs. To address the associated nonlinear two-dimensional Hamilton-Jacobi-Bellman (HJB) equation, we propose an innovative deep learning-driven policy iteration scheme with three key advantages: i) it has the potential to address the curse of dimensionality; ii) it is adaptable to problems involving high-dimensional control spaces; iii) it eliminates truncation errors. The numerical analysis of the proposed scheme, including convergence analysis in a general setting, is also discussed. To illustrate the impact of these two types of transaction costs on portfolio choice, we conduct through numerical experiments using three typical utility functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02267 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A deep learning-driven iterative scheme for high-dimensional HJB equations in portfolio selection with exogenous and endogenous costs Yan, Dong Zhang, Nanyi Guo, Junyi Mathematical Finance In this paper, we first conduct a study of the portfolio selection problem, incorporating both exogenous (proportional) and endogenous (resulting from liquidity risk, characterized by a stochastic process) transaction costs through the utility-based approach. We also consider the intrinsic relationship between these two types of costs. To address the associated nonlinear two-dimensional Hamilton-Jacobi-Bellman (HJB) equation, we propose an innovative deep learning-driven policy iteration scheme with three key advantages: i) it has the potential to address the curse of dimensionality; ii) it is adaptable to problems involving high-dimensional control spaces; iii) it eliminates truncation errors. The numerical analysis of the proposed scheme, including convergence analysis in a general setting, is also discussed. To illustrate the impact of these two types of transaction costs on portfolio choice, we conduct through numerical experiments using three typical utility functions. |
| title | A deep learning-driven iterative scheme for high-dimensional HJB equations in portfolio selection with exogenous and endogenous costs |
| topic | Mathematical Finance |
| url | https://arxiv.org/abs/2509.02267 |