Causal PDE-Control for Adaptive Portfolio Optimization under Partial Information

ArXiv ID: 2509.09585 “View on arXiv”

Authors: Alejandro Rodriguez Dominguez

Abstract

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.

Keywords: Causal Inference, Partial Differential Equations (PDE), Structural Breaks, Non-Stationary Markets, Asset Allocation

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced PDEs, nonlinear filtering, and stochastic calculus at a high density, scoring near the top for math complexity. It also presents a substantial empirical study on a 300+ driver U.S. equity panel with specific performance metrics, indicating strong data and implementation focus.

  flowchart TD
    A["Research Goal: Robust Adaptive Allocation under Partial Info"] --> B["Methodology: Causal PDE-Control Model<br/>Causal Drivers + Filtering + PDE Control"]
    B --> C["Data/Inputs: U.S. Equity Panel<br/>300+ Candidate Drivers<br/>Structural Break Regimes"]
    C --> D["Computational Process:<br/>Causal Driver Span Selection &<br/>Forward-Backward PDE Solver"]
    D --> E["Key Findings/Outcomes:<br/>1. Consistency via Causal Completeness<br/>2. Stability via Projection-Divergence Duality<br/>3. High Performance, Low Turnover<br/>4. Interpretable Limits (Markowitz, Black-Litterman)"]