Causal PDE-Control Models: A Structural Framework for Dynamic Portfolio Optimization

2025-09-11

AI Summary

Conventional portfolio models lack robustness under structural market breaks, while black-box machine learning approaches sacrifice economic interpretability. Method: We propose a dynamic optimization framework integrating causal inference, nonlinear filtering, and forward-backward stochastic differential equations (FBSDEs), grounded in physics-informed neural networks (PINNs) for efficient FBSDE control solving. Contribution/Results: Theoretically, we introduce conditional risk-neutral measures, projection-divergence duality, and causal completeness—establishing classical models as degenerate cases and unifying financial theory with data-driven paradigms. Empirically, the framework significantly outperforms econometric and machine learning benchmarks on global equity panel data, delivering higher Sharpe ratios, lower turnover, and enhanced premium persistence—all while preserving structural interpretability and distributional robustness in nonstationary environments.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems

Abstract

Classical portfolio models collapse under structural breaks, while modern machine-learning allocators adapt flexibly but often at the cost of transparency and interpretability. This paper introduces Causal PDE-Control Models (CPCMs), a unifying framework that integrates causal inference, nonlinear filtering, and forward-backward partial differential equations for dynamic portfolio optimization. The framework delivers three theoretical advances: (i) the existence of conditional risk-neutral measures under evolving information sets; (ii) a projection-divergence duality that quantifies the stability cost of departing from the causal driver manifold; and (iii) causal completeness, establishing that a finite driver span can capture all systematic premia. Classical methods such as Markowitz, CAPM, and Black-Litterman appear as degenerate cases, while reinforcement learning and deep-hedging policies emerge as unconstrained, symmetry-breaking approximations. Empirically, CPCM solvers implemented with physics-informed neural networks achieve higher Sharpe ratios, lower turnover, and more persistent premia than both econometric and machine-learning benchmarks, using a global equity panel with more than 300 candidate drivers. By reframing portfolio optimization around structural causality and PDE control, CPCMs provide a rigorous, interpretable, and computationally tractable foundation for robust asset allocation under nonstationary conditions.

Problem

• Integrates causal inference and PDEs for dynamic portfolio optimization
• Addresses structural breaks and interpretability in asset allocation
• Provides theoretical advances for robust nonstationary financial conditions

Innovation

• Causal inference and PDE control integration
• Physics-informed neural networks implementation
• Conditional risk-neutral measures under evolving information