Causal PDE-Control Models for Dynamic Portfolio Optimization with Latent Drivers

Abstract

Classical portfolio models degrade under structural breaks, whereas flexible machine-learning allocation methods often lack arbitrage consistency and interpretability. We propose Causal PDE-Control Models (CPCMs), a framework that integrates structural causal drivers, nonlinear filtering, and forward-backward PDE control to produce robust and transparent allocation rules under partial information. We construct driver-conditional risk-neutral measures on the observable filtration via filtering together with the corresponding martingale representation, linking pricing, hedging, and portfolio choice under a common information set. We further establish a projection-divergence duality showing that restricting portfolios to the causal driver span selects the feasible allocation closest to the unconstrained optimum under a convex divergence, thereby quantifying the stability cost of deviations from the causal manifold, and derive a causal completeness condition identifying when a finite driver span captures systematic premia. Markowitz, CAPM/APT, and Black-Litterman arise as limiting cases, while reinforcement learning and deep hedging appear as unconstrained approximations within the same pricing-control geometry. Empirically, on a U.S.equity panel with more than 300 candidate drivers, CPCM solvers achieve higher Sharpe ratios, lower turnover, and more persistent premia than econometric and machine-learning benchmarks.