Breaking the Dimensional Barrier: Dynamic Portfolio Choice with Parameter Uncertainty via Pontryagin Projection
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| Format: | Preprint |
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2026
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| author | Huh, Jeonggyu Koo, Hyeng Keun |
| author_facet | Huh, Jeonggyu Koo, Hyeng Keun |
| contents | We study continuous-time CRRA portfolio choice in diffusion markets with estimated and hence uncertain coefficients. Nature draws a latent parameter $θ\sim q$ at time $0$ and keeps it fixed; the investor never observes $θ$ and must commit to a single $θ$-blind policy maximizing an ex-ante objective, treating $q$ as a decision-time input. We propose a simulation-only two-stage solver.Stage 1 (DPO) performs BPTT-based stochastic gradient ascent through an Euler simulator while sampling $θ$ only inside the simulator. Stage 2 (Pontryagin projection) aggregates costate blocks across $θ\sim q$ and enforces the $q$-aggregated stationarity condition within the deployable class; the resulting correction can be amortized via interactive distillation. We refer to the full Stage 1 + Stage 2 pipeline as PG-DPO.We prove a uniform conditional BPTT-PMP correspondence and a residual-based policy-gap bound with explicit discretization and Monte Carlo error terms. Experiments on high-dimensional Gaussian drift-uncertainty and factor-driven benchmarks show that projection stabilizes learning and accurately recovers analytic decision-time references, while a model-free PPO baseline remains far from the targets. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_03175 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Breaking the Dimensional Barrier: Dynamic Portfolio Choice with Parameter Uncertainty via Pontryagin Projection Huh, Jeonggyu Koo, Hyeng Keun Computational Finance We study continuous-time CRRA portfolio choice in diffusion markets with estimated and hence uncertain coefficients. Nature draws a latent parameter $θ\sim q$ at time $0$ and keeps it fixed; the investor never observes $θ$ and must commit to a single $θ$-blind policy maximizing an ex-ante objective, treating $q$ as a decision-time input. We propose a simulation-only two-stage solver.Stage 1 (DPO) performs BPTT-based stochastic gradient ascent through an Euler simulator while sampling $θ$ only inside the simulator. Stage 2 (Pontryagin projection) aggregates costate blocks across $θ\sim q$ and enforces the $q$-aggregated stationarity condition within the deployable class; the resulting correction can be amortized via interactive distillation. We refer to the full Stage 1 + Stage 2 pipeline as PG-DPO.We prove a uniform conditional BPTT-PMP correspondence and a residual-based policy-gap bound with explicit discretization and Monte Carlo error terms. Experiments on high-dimensional Gaussian drift-uncertainty and factor-driven benchmarks show that projection stabilizes learning and accurately recovers analytic decision-time references, while a model-free PPO baseline remains far from the targets. |
| title | Breaking the Dimensional Barrier: Dynamic Portfolio Choice with Parameter Uncertainty via Pontryagin Projection |
| topic | Computational Finance |
| url | https://arxiv.org/abs/2601.03175 |