Scalable Pontryagin-Guided Adjoint-to-Control Recovery for Constrained Dynamic Portfolio Choice

We develop a scalable adjoint-to-control framework for continuous-time portfolio choice under smooth pointwise constraints. A feasible direct-policy-optimization (DPO) policy supplies rollouts; after training, fixed-latent open-loop BPTT (OL-BPTT) yields first- and second-order pathwise sensitivities, whose conditional projections produce adapted adjoint inputs. A nested antithetic common-random-number regression estimates the shifted wealth-row martingale input, and deployment solves the local generalized-Hamiltonian problem by an exact QP for quadratic-affine blocks or by a log barrier otherwise. We prove an OL-BPTT--PMP correspondence retaining orthogonal projection residuals, a local barrier--KKT approximation, and a performance-to-adjoint bridge under local quadratic growth. In an n=100 constrained Merton benchmark, the learned first adjoint has 0.46% mean relative error; under the analytical policy, the first adjoint, wealth curvature, and Brownian coefficient have nRMSEs of 0.031%, 0.035%, and 0.326%. In a terminal-only predictable-return CRRA benchmark, wealth homogeneity gives $P^{X\bullet,*}=D^2_{X\bullet}V$ and $ζ^{X,*}=0$. At the primary $512\times16$ projection budget, the full estimated-shift decoder has policy RMSE below $8.5\times10^{-3}$, while the benchmark-specific zero-shift oracle is below $2\times10^{-4}$. Across constraint, factor, barrier, and switching-region audits, recovery sharply reduces local KKT residuals and remains practical for portfolios with up to 100 risky assets.