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.

翻译：投资组合优化是金融数学中普遍存在的问题，其依赖于对资产收益协方差矩阵的精确估计。然而，成对协方差的估计效果可能欠佳，且为数字计算机计算时间敏感的最优投资组合能耗巨大。我们提出了一种节能、快速且完全模拟的流水线来解决投资组合优化问题，克服了这些限制。该模拟范式利用物理学基本原理，通过两步过程恢复精确的最优投资组合。首先，我们利用平衡传播（反向传播的模拟替代方法）训练线性自编码器神经网络，以计算低秩协方差矩阵。随后，模拟连续Hopfield网络输出给定期望收益下的最小方差投资组合。整个有效前沿可由此恢复，并可根据风险偏好选择最优投资组合。