A Fully Analog Pipeline for Portfolio Optimization

ArXiv ID: 2411.06566 “View on arXiv”

Authors: Unknown

Abstract

Portfolio optimization is a ubiquitous problem in financial mathematics that relies on accurate estimates of covariance matrices for asset returns. However, estimates of pairwise covariance could be better and calculating time-sensitive optimal portfolios is energy-intensive for digital computers. We present an energy-efficient, fast, and fully analog pipeline for solving portfolio optimization problems that overcomes these limitations. The analog paradigm leverages the fundamental principles of physics to recover accurate optimal portfolios in a two-step process. Firstly, we utilize equilibrium propagation, an analog alternative to backpropagation, to train linear autoencoder neural networks to calculate low-rank covariance matrices. Then, analog continuous Hopfield networks output the minimum variance portfolio for a given desired expected return. The entire efficient frontier may then be recovered, and an optimal portfolio selected based on risk appetite.

Keywords: Portfolio Optimization, Equilibrium Propagation, Linear Autoencoder, Analog Computing, Efficient Frontier, Multi-Asset (Portfolio)

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail
  • Why: The paper introduces advanced analog computational methods (continuous Hopfield networks and equilibrium propagation) with detailed mathematical derivations of energy functions and dynamics, while demonstrating the pipeline with empirical data sampling and noise modeling.
  flowchart TD
    A["Research Goal<br>Energy-Efficient Portfolio<br>Optimization"] --> B["Input: Asset Return Data"]
    B --> C["Step 1: Low-Rank Covariance<br>via Analog Linear Autoencoder"]
    C --> D["Training: Equilibrium Propagation<br>Physics-Based Analog Backpropagation"]
    D --> E["Step 2: Optimization<br>via Analog Continuous Hopfield Network"]
    E --> F["Output: Minimum Variance<br>Portfolio for Target Return"]
    F --> G["Outcome: Efficient Frontier &<br>Optimal Portfolio Selection"]