Paper: arXiv 2507.07159

Authors: Nishan Ranabhat, Behnam Javanparast, David Goerz, Estelle Inack

Abstract

Portfolio optimization is a routine asset management operation conducted in financial institutions around the world. However, under real-world constraints such as turnover limits and transaction costs, its formulation becomes a mixed-integer nonlinear program that current mixed-integer optimizers often struggle to solve. We propose mapping this problem onto a classical Ising-like Hamiltonian and solving it with Variational Neural Annealing (VNA), via its classical formulation implemented using autoregressive neural networks. We demonstrate that VNA can identify near-optimal solutions for portfolios comprising more than 2,000 assets and yields performance comparable to that of state-of-the-art optimizers, such as Mosek, while exhibiting faster convergence on hard instances. Finally, we present a dynamical finite-size scaling analysis applied to the S&P 500, Russell 1000, and Russell 3000 indices, revealing universal behavior and polynomial annealing time scaling of the VNA algorithm on portfolio optimization problems.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces high-level mathematical concepts such as Ising Hamiltonian mapping, variational neural annealing, and dynamical finite-size scaling, demonstrating substantial theoretical depth. It validates its approach with large-scale backtests on major indices (S&P 500, Russell 1000/3000) and benchmarks against commercial solvers like Mosek, showing strong empirical implementation and performance analysis.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Optimize portfolios with constraints<br>over 2,000 assets"] --> B["Methodology<br>Variational Neural Annealing<br>Autoregressive Neural Networks"]
  B --> C["Formulation<br>Map to Ising-like Hamiltonian<br>Mixed-Integer Nonlinear Program"]
  C --> D["Data Sources<br>S&P 500, Russell 1000,<br>Russell 3000 Indices"]
  D --> E["Computational Process<br>Dynamical Finite-Size Scaling Analysis"]
  E --> F{"Findings"}
  F --> G["Near-optimal solutions<br>Comparable to Mosek<br>Faster on hard instances"]
  F --> H["Scaling Laws<br>Universal behavior revealed<br>Polynomial annealing time"]