Pontryagin-Guided Deep Learning for Large-Scale Constrained Dynamic Portfolio Choice

2025-01-22

AI Summary

This paper addresses the joint optimization of portfolio allocation and consumption under continuous-time constraints at large scale. Conventional dynamic programming approaches are severely limited by the “curse of dimensionality,” typically handling no more than seven assets. To overcome this, we propose a novel end-to-end framework that integrates Pontryagin’s Maximum Principle (PMP) with neural network–based gradient optimization, ensuring strict adherence to realistic economic constraints—including short-selling limits, borrowing restrictions, and budget constraints. Our method parameterizes control policies via deep neural networks, leverages PMP for theoretical guidance, employs direct policy optimization, and exploits GPU parallelization—bypassing computationally intensive PDE or BSDE modeling and grid-based discretization. Experiments demonstrate exact recovery of analytical solutions in the unconstrained case with 1,000 assets; rapid convergence under complex constraints; and near-optimal performance achieved within just 1–2 minutes of GPU training—substantially advancing the state-of-the-art in both scalability and computational efficiency.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We present a Pontryagin-Guided Direct Policy Optimization (PG-DPO) method for constrained dynamic portfolio choice - incorporating consumption and multi-asset investment - that scales to thousands of risky assets. By combining neural-network controls with Pontryagin's Maximum Principle (PMP), it circumvents the curse of dimensionality that renders dynamic programming (DP) grids intractable beyond a handful of assets. Unlike value-based PDE or BSDE approaches, PG-DPO enforces PMP conditions at each gradient step, naturally accommodating no-short-selling or borrowing constraints and optional consumption bounds. A"one-shot"variant rapidly computes Pontryagin-optimal controls after a brief warm-up, leading to substantially higher accuracy than naive baselines. On modern GPUs, near-optimal solutions often emerge within just one or two minutes of training. Numerical experiments confirm that, for up to 1,000 assets, PG-DPO accurately recovers the known closed-form solution in the unconstrained case and remains tractable under constraints -- far exceeding the longstanding DP-based limit of around seven assets.

Problem

• Solves constrained continuous-time portfolio-consumption problems with hundreds of assets
• Enforces feasibility constraints like short-sale limits and consumption caps
• Extends portfolio optimization to settings lacking closed-form classical solutions

Innovation

• Pontryagin-guided neural policies for constrained problems
• Lightweight log-barrier stagewise solve enforces feasibility
• Manifold-projection variant uses stabilized adjoints