Machine-learning a family of solutions to an optimal pension investment problem

ArXiv ID: 2511.07045 “View on arXiv”

Authors: John Armstrong, Cristin Buescu, James Dalby, Rohan Hobbs

Abstract

We use a neural network to identify the optimal solution to a family of optimal investment problems, where the parameters determining an investor’s risk and consumption preferences are given as inputs to the neural network in addition to economic variables. This is used to develop a practical tool that can be used to explore how pension outcomes vary with preference parameters. We use a Black-Scholes economic model so that we may validate the accuracy of network using a classical and provably convergent numerical method developed using the duality approach.

Keywords: Deep Learning, Optimal Portfolio Selection, Utility Maximization, Duality Methods, Pension Planning

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper employs advanced mathematics including stochastic differential equations, Itô’s lemma, exponential utility functions, and duality approaches for solving a high-dimensional optimization problem. However, it relies on a simplified Black-Scholes model for validation and focuses on theoretical numerical methods without presenting backtests, real-world data, or implementation-heavy empirical results.

  flowchart TD
    A["Research Goal:<br>Identify optimal pension investment solutions<br>for a family of preference parameters"] --> B["Data & Inputs:<br>Economic Model: Black-Scholes<br>Preferences: Risk & Consumption parameters"]
    
    B --> C1["ML Methodology:<br>Neural Network Training<br>using duality-based optimization"]
    B --> C2["Validation Methodology:<br>Classical Numerical Solver<br>for ground truth comparison"]
    
    C1 --> D["Computational Process:<br>Neural Network approximates<br>optimal investment strategy function"]
    C2 --> D
    
    D --> E["Key Findings:<br>1. Validated NN accuracy vs. classical method<br>2. Developed practical tool for exploring<br>pension outcomes vs. preferences<br>3. Generalizable family of solutions"]