Causal PDE-Control Models for Dynamic Portfolio Optimization with Latent Drivers
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arXiv
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| Format: | Preprint |
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2025
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| author | Dominguez, Alejandro Rodriguez |
| author_facet | Dominguez, Alejandro Rodriguez |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_09585 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Causal PDE-Control Models for Dynamic Portfolio Optimization with Latent Drivers Dominguez, Alejandro Rodriguez Portfolio Management G.1.6; G.1.8; G.1.10; G.3; I.2.6; I.5.3; I.5.4; I.6.5; J.2; J.4; J.6 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. |
| title | Causal PDE-Control Models for Dynamic Portfolio Optimization with Latent Drivers |
| topic | Portfolio Management G.1.6; G.1.8; G.1.10; G.3; I.2.6; I.5.3; I.5.4; I.6.5; J.2; J.4; J.6 |
| url | https://arxiv.org/abs/2509.09585 |