Portfolio Optimization with Feedback Strategies Based on Artificial Neural Networks

ArXiv ID: 2411.09899 “View on arXiv”

Authors: Unknown

Abstract

With the recent advancements in machine learning (ML), artificial neural networks (ANN) are starting to play an increasingly important role in quantitative finance. Dynamic portfolio optimization is among many problems that have significantly benefited from a wider adoption of deep learning (DL). While most existing research has primarily focused on how DL can alleviate the curse of dimensionality when solving the Hamilton-Jacobi-Bellman (HJB) equation, some very recent developments propose to forego derivation and solution of HJB in favor of empirical utility maximization over dynamic allocation strategies expressed through ANN. In addition to being simple and transparent, this approach is universally applicable, as it is essentially agnostic about market dynamics. To showcase the method, we apply it to optimal portfolio allocation between a cash account and the S&P 500 index modeled using geometric Brownian motion or the Heston model. In both cases, the results are demonstrated to be on par with those under the theoretical optimal weights assuming isoelastic utility and real-time rebalancing. A set of R codes for a broad class of stochastic volatility models are provided as a supplement.

Keywords: Deep Learning (DL), Portfolio Optimization, Hamilton-Jacobi-Bellman (HJB), Geometric Brownian Motion, Heston Model, Equities

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematics including stochastic differential equations, Hamilton-Jacobi-Bellman equations, and neural network theory, yet provides a backtest-ready framework with R code and validation on S&P 500 and VIX data.

  flowchart TD
    A["Research Goal: <br>Dynamic Portfolio Optimization with ANN"] --> B["Key Methodology: <br>Empirical Utility Maximization via ANN"]
    B --> C["Data & Inputs: <br>S&P 500 & Cash via GBM/Heston Models"]
    C --> D["Computational Process: <br>Train ANN to Maximize Cumulative Utility"]
    D --> E{"Key Findings & Outcomes"}
    E --> F["ANN strategies match <br>theoretical optimal weights"]
    E --> G["Method is model-agnostic <br>and avoids solving HJB"]
    E --> H["Code provided for <br>stochastic volatility models"]