Breaking the Dimensional Barrier: A Pontryagin-Guided Direct Policy Optimization for Continuous-Time Multi-Asset Portfolio Choice
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915488889569280 |
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| author | Huh, Jeonggyu Jeon, Jaegi Koo, Hyeng Keun Lim, Byung Hwa |
| author_facet | Huh, Jeonggyu Jeon, Jaegi Koo, Hyeng Keun Lim, Byung Hwa |
| contents | We introduce the Pontryagin-Guided Direct Policy Optimization (PG-DPO) framework for high-dimensional continuous-time portfolio choice. Our approach combines Pontryagin's Maximum Principle (PMP) with backpropagation through time (BPTT) to directly inform neural network-based policy learning, enabling accurate recovery of both myopic and intertemporal hedging demands--an aspect often missed by existing methods. Building on this, we develop the Projected PG-DPO (P-PGDPO) variant, which achieves nearoptimal policies with substantially improved efficiency. P-PGDPO leverages rapidly stabilizing costate estimates from BPTT and analytically projects them onto PMP's first-order conditions, reducing training overhead while improving precision. Numerical experiments show that PG-DPO matches or exceeds the accuracy of Deep BSDE, while P-PGDPO delivers significantly higher precision and scalability. By explicitly incorporating time-to-maturity, our framework naturally applies to finite-horizon problems and captures horizon-dependent effects, with the long-horizon case emerging as a stationary special case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11116 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Breaking the Dimensional Barrier: A Pontryagin-Guided Direct Policy Optimization for Continuous-Time Multi-Asset Portfolio Choice Huh, Jeonggyu Jeon, Jaegi Koo, Hyeng Keun Lim, Byung Hwa Portfolio Management Computational Finance We introduce the Pontryagin-Guided Direct Policy Optimization (PG-DPO) framework for high-dimensional continuous-time portfolio choice. Our approach combines Pontryagin's Maximum Principle (PMP) with backpropagation through time (BPTT) to directly inform neural network-based policy learning, enabling accurate recovery of both myopic and intertemporal hedging demands--an aspect often missed by existing methods. Building on this, we develop the Projected PG-DPO (P-PGDPO) variant, which achieves nearoptimal policies with substantially improved efficiency. P-PGDPO leverages rapidly stabilizing costate estimates from BPTT and analytically projects them onto PMP's first-order conditions, reducing training overhead while improving precision. Numerical experiments show that PG-DPO matches or exceeds the accuracy of Deep BSDE, while P-PGDPO delivers significantly higher precision and scalability. By explicitly incorporating time-to-maturity, our framework naturally applies to finite-horizon problems and captures horizon-dependent effects, with the long-horizon case emerging as a stationary special case. |
| title | Breaking the Dimensional Barrier: A Pontryagin-Guided Direct Policy Optimization for Continuous-Time Multi-Asset Portfolio Choice |
| topic | Portfolio Management Computational Finance |
| url | https://arxiv.org/abs/2504.11116 |