Portfolio Optimization: A Neurodynamic Approach Based on Spiking Neural Networks

Area of Science:

• Computational Finance
• Biomimetics
• Artificial Intelligence

Background:

• Portfolio optimization is crucial for balancing risk and return in finance.
• Incorporating transaction costs and cardinality limits transforms it into a complex mixed-integer quadratic program.
• Traditional methods struggle with the computational demands of these complex optimization problems.

Purpose of the Study:

• To develop an efficient algorithm for complex portfolio optimization problems by drawing inspiration from biological neural systems.
• To reformulate the mixed-integer quadratic programming problem as a constrained quadratic program solvable by spiking neural network dynamics.
• To establish a biomimetic pathway for solving computationally intensive financial optimization tasks.

Main Methods:

• Reformulated portfolio optimization as a constrained quadratic program.
• Developed a solver using dynamics inspired by leaky integrate-and-fire spiking neural networks (SNNs).
• Implemented a solver alternating between continuous gradient flow and discrete constraint projections.
• Evaluated the SNN solver on portfolios of 5 to 50 assets using five years of market data, comparing against ECOS_BB, OSQP, and particle swarm optimization (PSO).

Main Results:

• The SNN solver achieved the highest daily expected return (0.261%) on a 50-asset portfolio, outperforming exact mixed-integer quadratic programming (MIQP) (0.225%) and PSO (0.092%).
• Runtimes varied from 0.5 s for small portfolios to 8.4 s for large, high-quality schedules.
• While current Python runtimes are comparable to existing methods, the approach demonstrates potential for significant speedups on specialized neuromorphic hardware.

Conclusions:

• Spiking neural network dynamics offer a promising biomimetic approach to solving complex portfolio optimization problems.
• This method provides a pathway towards real-time portfolio rebalancing through potential deployment on neuromorphic hardware.
• The SNN solver demonstrates competitive performance and potential for future advancements in financial optimization.