Paper: arXiv 2407.17645

Abstract

We present the first application of modern Hopfield networks to the problem of portfolio optimization. We performed an extensive study based on combinatorial purged cross-validation over several datasets and compared our results to both traditional and deep-learning-based methods for portfolio selection. Compared to state-of-the-art deep-learning methods such as Long-Short Term Memory networks and Transformers, we find that the proposed approach performs on par or better, while providing faster training times and better stability. Our results show that Modern Hopfield Networks represent a promising approach to portfolio optimization, allowing for an efficient, scalable, and robust solution for asset allocation, risk management, and dynamic rebalancing.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.0/10 (capped from 8.0: transaction costs not modelled; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces advanced deep learning architectures like Modern Hopfield Networks, which involve sophisticated energy-based models and attention mechanisms, indicating high math complexity. It also demonstrates strong empirical rigor through extensive combinatorial purged cross-validation, comparison against state-of-the-art baselines, and reporting of multiple financial metrics like Sharpe and Sortino ratios.

Research Flowchart

  flowchart TD
  A["Research Goal: Apply Modern Hopfield Networks<br>to Portfolio Optimization"] --> B["Data Input: Multiple Datasets<br>Equities Asset Allocation"]
  B --> C["Methodology: Combinatorial<br>Purged Cross-Validation"]
  C --> D["Computational Process:<br>Modern Hopfield Networks"]
  D --> E["Comparison: vs. LSTM & Transformers<br>Traditional Methods"]
  E --> F["Key Findings:<br>On Par or Better Performance"]
  E --> G["Key Findings:<br>Faster Training & Better Stability"]
  F --> H["Outcomes: Efficient, Scalable<br>Robust Asset Allocation Solution"]
  G --> H

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and 39 more
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1 of 47 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.