Paper: arXiv 2412.13101

Authors: Jeonggyu Huh, Jaegi Jeon

Abstract

We present a Pontryagin-Guided Direct Policy Optimization (PG-DPO) framework for Merton’s portfolio problem, unifying modern neural-network-based policy parameterization with the adjoint viewpoint from Pontryagin’s maximum principle (PMP). Instead of approximating the value function (as done in deep BSDE methods), we track a policy-fixed BSDE for the adjoint processes, which allows each gradient update to align with continuous-time PMP conditions. This setup yields locally optimal consumption and investment policies that are closely tied to classical stochastic control. We further incorporate an alignment penalty that nudges the learned policy toward Pontryagin-derived solutions, enhancing both convergence speed and training stability. Numerical experiments confirm that PG-DPO effectively handles both consumption and investment, achieving strong performance and interpretability without requiring large offline datasets or model-free reinforcement learning.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 5.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical integration of Pontryagin’s Maximum Principle with deep policy optimization for portfolio choice with both investment and consumption. It rigorously sets up the FBSDE/adjoint framework and provides local convergence insights using Robbins-Monro stochastic approximation theory. While the empirical validation is mostly numerical simulation against known analytical baselines rather than messy real-world market datasets, it is theoretically sound and well-constructed.

Research Flowchart

  flowchart TD
    A[Goal: Solve Merton's Portfolio Problem via Pontryagin-Guided Policy Optimization] --> B[Inputs: Continuous-time Market Dynamics & Utility Functions]
    B --> C[Parameterize Investment/Consumption Policy with Neural Networks]
    C --> D[Track Policy-Fixed BSDE for Adjoint Processes]
    D --> E[Apply Alignment Penalty to Nudge Policy toward PMP Conditions]
    E --> F[Direct Policy Gradient Updates Optimization]
    F --> G[Outcomes: Stable Convergence to Locally Optimal Policies without Large Datasets]

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1 of 50 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.