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This paper presents a novel framework for optimal portfolio selection in large financial markets using Mean Field Game (MFG) theory coupled with Physics-Informed Neural Networks (PINNs). We extend the classical Merton problem to a multi-agent setting where investors interact through mean-field effects on asset prices. The resulting coupled Hamilton-Jacobi-Bellman (HJB) and Fokker-Planck (FP) system is solved numerically using PINNs, demonstrating how deep learning can circumvent traditional computational challenges in high-dimensional MFG problems. Our approach captures endogenous price formation and provides insights into collective market behavior.

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Mean Field Game Approach to Multi-asset Portfolio Optimization with Physics-Informed Neural Networks

  • 会议论文

  • 发表日期：

    2026年

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  • John Freddy Moreno Trujillo

摘要

This paper presents a novel framework for optimal portfolio selection in large financial markets using Mean Field Game (MFG) theory coupled with Physics-Informed Neural Networks (PINNs). We extend the classical Merton problem to a multi-agent setting where investors interact through mean-field effects on asset prices. The resulting coupled Hamilton-Jacobi-Bellman (HJB) and Fokker-Planck (FP) system is solved numerically using PINNs, demonstrating how deep learning can circumvent traditional computational challenges in high-dimensional MFG problems. Our approach captures endogenous price formation and provides insights into collective market behavior.