Causal PDE-Control for Adaptive Portfolio Optimization under Partial Information

Classical portfolio models tend to degrade under structural breaks, whereas flexible machine-learning allocators often lack arbitrage consistency and interpretability. We propose Causal PDE-Control Models (CPCMs), a framework that links structural causal drivers, nonlinear filtering, and forward-backward PDE control to produce robust, transparent allocation rules under partial information. The main contributions are: (i) construction of scenario-conditional risk-neutral measures on the observable filtration via filtering, with an associated martingale representation; (ii) a projection-divergence duality that quantifies stability costs when deviating from the causal driver span; (iii) a causal completeness condition showing when a finite driver span captures systematic premia; and (iv) conformal transport and smooth subspace evolution guaranteeing time-consistent projections on a moving driver manifold. Markowitz, CAPM/APT, and Black-Litterman arise as limit or constrained cases; reinforcement learning and deep hedging appear as unconstrained approximations once embedded in the same pricing-control geometry. On a U.S. equity panel with 300+ candidate drivers, CPCM solvers achieve higher performance, lower turnover, and more persistent premia than econometric and ML benchmarks, offering a rigorous and interpretable basis for dynamic asset allocation in nonstationary markets.