Breaking the Dimensional Barrier: Dynamic Portfolio Choice with Parameter Uncertainty via Pontryagin Projection

We study continuous-time CRRA portfolio choice in diffusion markets with uncertain estimated coefficients. Nature draws a latent parameter from a given distribution and keeps it fixed; the investor cannot observe this parameter and must commit to a parameter-blind policy maximizing an ex-ante objective. We treat the uncertainty distribution as an inference-agnostic sampling input. We develop a simulation-only two-stage solver. Stage 1 extends Pontryagin-Guided Direct Policy Optimization (PG-DPO) by sampling parameters internally and computing gradients via backpropagation through time. Stage 2 performs an aggregated Pontryagin projection: it aggregates costates across the parameter distribution to enforce a deployable stationarity condition, yielding a structured correction amortized via interactive distillation. We prove a uniform conditional BPTT-PMP correspondence and a residual-based policy-gap bound with explicit error terms. Experiments on high-dimensional Gaussian drift and factor-driven benchmarks show that projection stabilizes learning and accurately recovers analytic references, while a model-free PPO baseline remains far from the targets.