Breaking the Dimensional Barrier for Constrained Dynamic Portfolio Choice

Abstract

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($\epsilon$) 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.