Portfolio Optimization: A Neurodynamic Approach Based on Spiking Neural Networks.

Portfolio optimization is fundamental to modern finance, enabling investors to construct allocations that balance risk and return while satisfying practical constraints. When transaction costs and cardinality limits are incorporated, the problem becomes a computationally demanding mixed-integer quadratic program. This work demonstrates how principles from biomimetics-specifically, the computational strategies employed by biological neural systems-can inspire efficient algorithms for complex optimization problems. We demonstrate that this problem can be reformulated as a constrained quadratic program and solved using dynamics inspired by spiking neural networks. Building on recent theoretical work showing that leaky integrate-and-fire dynamics naturally implement projected gradient descent for convex optimization, we develop a solver that alternates between continuous gradient flow and discrete constraint projections. By mimicking the event-driven, energy-efficient computation observed in biological neurons, our approach offers a biomimetic pathway to solving computationally intensive financial optimization problems. We implement the approach in Python and evaluate it on portfolios of 5 to 50 assets using five years of market data, comparing solution quality against mixed-integer solvers (ECOS_BB), convex relaxations (OSQP), and particle swarm optimization. Experimental results demonstrate that the SNN solver achieves the highest expected return (0.261% daily) among all evaluated methods on the 50-asset portfolio, outperforming exact MIQP (0.225%) and PSO (0.092%), with runtimes ranging from 0.5 s for small portfolios to 8.4 s for high-quality schedules on large portfolios. While current Python runtimes are comparable to existing approaches, the key contribution is establishing a path to neuromorphic hardware deployment: specialized SNN processors could execute these dynamics orders of magnitude faster than conventional architectures, enabling real-time portfolio rebalancing at institutional scale.