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arXiv · 2504.11116

Breaking the Dimensional Barrier: A Pontryagin-Guided Direct Policy Optimization for Continuous-Time Multi-Asset Portfolio Choice

Jeonggyu Huh·Jaegi Jeon·Hyeng Keun Koo·Byung Hwa Lim
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Abstract

We introduce the Pontryagin-Guided Direct Policy Optimization (PG-DPO) framework for high-dimensional continuous-time portfolio choice. Our approach combines Pontryagin's Maximum Principle (PMP) with backpropagation through time (BPTT) to directly inform neural network-based policy learning, enabling accurate recovery of both myopic and intertemporal hedging demands--an aspect often missed by existing methods. Building on this, we develop the Projected PG-DPO (P-PGDPO) variant, which achieves nearoptimal policies with substantially improved efficiency. P-PGDPO leverages rapidly stabilizing costate estimates from BPTT and analytically projects them onto PMP's first-order conditions, reducing training overhead while improving precision. Numerical experiments show that PG-DPO matches or exceeds the accuracy of Deep BSDE, while P-PGDPO delivers significantly higher precision and scalability. By explicitly incorporating time-to-maturity, our framework naturally applies to finite-horizon problems and captures horizon-dependent effects, with the long-horizon case emerging as a stationary special case.

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Jeonggyu Huh, Jaegi Jeon, Hyeng Keun Koo, Byung Hwa Lim. 2025-04-15. Breaking the Dimensional Barrier: A Pontryagin-Guided Direct Policy Optimization for Continuous-Time Multi-Asset Portfolio Choice. https://arxiv.org/abs/2504.11116

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