Breaking the Dimensional Barrier for Constrained Dynamic Portfolio Choice
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909888511213568 |
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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 propose a scalable, policy-centric framework for continuous-time multi-asset portfolio-consumption optimization under inequality constraints. Our method integrates neural policies with Pontryagin's Maximum Principle (PMP) and enforces feasibility by maximizing a log-barrier-regularized Hamiltonian at each time-state pair, thereby satisfying KKT conditions without value-function grids. Theoretically, we show that the barrier-regularized Hamiltonian yields O($ε$) policy error and a linear Hamiltonian gap (quadratic when the KKT solution is interior), and we extend the BPTT-PMP correspondence to constrained settings with stable costate convergence. Empirically, PG-DPO and its projected variant (P-PGDPO) recover KKT-optimal policies in canonical short-sale and consumption-cap problems while maintaining strict feasibility across dimensions; unlike PDE/BSDE solvers, runtime scales linearly with the number of assets and remains practical at n=100. These results provide a rigorous and scalable foundation for high-dimensional constrained continuous-time portfolio optimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12600 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Breaking the Dimensional Barrier for Constrained Dynamic Portfolio Choice Huh, Jeonggyu Jeon, Jaegi Koo, Hyeng Keun Lim, Byung Hwa Portfolio Management We propose a scalable, policy-centric framework for continuous-time multi-asset portfolio-consumption optimization under inequality constraints. Our method integrates neural policies with Pontryagin's Maximum Principle (PMP) and enforces feasibility by maximizing a log-barrier-regularized Hamiltonian at each time-state pair, thereby satisfying KKT conditions without value-function grids. Theoretically, we show that the barrier-regularized Hamiltonian yields O($ε$) policy error and a linear Hamiltonian gap (quadratic when the KKT solution is interior), and we extend the BPTT-PMP correspondence to constrained settings with stable costate convergence. Empirically, PG-DPO and its projected variant (P-PGDPO) recover KKT-optimal policies in canonical short-sale and consumption-cap problems while maintaining strict feasibility across dimensions; unlike PDE/BSDE solvers, runtime scales linearly with the number of assets and remains practical at n=100. These results provide a rigorous and scalable foundation for high-dimensional constrained continuous-time portfolio optimization. |
| title | Breaking the Dimensional Barrier for Constrained Dynamic Portfolio Choice |
| topic | Portfolio Management |
| url | https://arxiv.org/abs/2501.12600 |