Paper: arXiv 2511.07045

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.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: 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.

Research Flowchart

  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"]

Cited References (81)

  1. X marks the bank: digitalisation and depositor runs (2025)
  2. Directed Scale-Free Graphs (2003) — link
  3. Pareto’s Law of Income Distribution: Evidence for Germany, the United Kingdom, and the United States (2005) — link
  4. Do wealth distributions follow power laws? Evidence from ‘rich lists’ (2014) — link
  5. The Double Pareto-Lognormal Distribution—A New Parametric Model for Size Distributions (2004) — link
  6. A comparison of the effectiveness of alternative DC and CDC designs in a UK market (2026) — link
  7. Optimal post-retirement investment and consumption under longevity risk in collective funds (2025) — link
  8. Demand–Deposit Contracts and the Probability of Bank Runs (2005) — link
and 73 more
  1. Bank Runs, Deposit Insurance, and Liquidity (1983)
  2. Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks (1998) — link
  3. Global Games and Equilibrium Selection (1993) — link
  4. Utility Theory Front To Back — Inferring Utility From Agents’ Choices (2014) — link
  5. Importance sampling for option pricing with feedforward neural networks (2025) — link
  6. Social Media as a Bank Run Catalyst (2024) — link
  7. Statistical mechanics of complex networks (2002) — link
  8. The Structure and Function of Complex Networks (2003) — link
  9. On Random Graphs I (1959)
  10. Intergenerational cross-subsidies in UK collective defined contribution (CDC) funds (2024) — link
  11. Collectivised Post-Retirement Investment (2020) — link
  12. Collectivised Pension Investment with Exponential Kihlstrom–Mirman Preferences (2019) — link
  13. Optimal consumption and portfolio choice for pooled annuity funds (2008)
  14. An elementary approach to the Merton problem (2021)
  15. Theory of Games and Economic Behavior (1947)
  16. A Note on the Pure Theory of Consumer’s Behaviour (1938)
  17. The Construction of Utility Functions from Expenditure Data (1967)
  18. The Nonparametric Approach to Demand Analysis (1982)
  19. Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles (2004) — link
  20. Long-run risks and financial markets (2007) — link
  21. Explaining asset pricing puzzles associated with the 1987 market crash (2011) — link
  22. Optimal mutual insurance against systematic longevity risk — → 2410.07749
  23. The infinite-horizon investment-consumption problem for Epstein-Zin stochastic differential utility. II (2023) — link
  24. The infinite horizon investment-consumption problem for Epstein-Zin stochastic differential utility. I : Foundations (2023) — link
  25. Optimal consumption and investment with Epstein–Zin recursive utility (2017)
  26. King William’s Tontine: Why the Retirement Annuity of the Future Should Resemble its Past (2015)
  27. Optimal retirement income tontines (2015) — link
  28. Modern tontine with bequest: Innovation in pooled annuity products (2019) — link
  29. Bringing cost transparency to the life annuity market (2014) — link
  30. Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case (1969)
  31. Dynamic Programming (1957)
  32. Continuous-time Stochastic Control and Optimization with Financial Applications (2009)
  33. Learning a functional control for high-frequency finance (2022) — link
  34. Uncovering Utility Functions from Observed Outcomes (2025) — link
  35. Uncertain lifetime and intertemporal choice: risk aversion as a rationale for time discounting (2006)
  36. Temporal resolution of uncertainty and dynamic choice theory (1978)
  37. Classifying Markets up to Isomorphism (2018) — link
  38. Convex Analysis (2015)
  39. Optimization by vector space methods (1997)
  40. Grouping individual investment preferences in retirement savings: A cluster analysis of a USS members risk attitude survey (2020) — link
  41. Destabilisation of bank deposits across destinations: assessment and policy implications (2024) — link
  42. Understanding the Speed and Size of Bank Runs in Historical Comparison (2023) — link
  43. A Monetary History of the United States, 1867-1960 (1963)
  44. Securitized banking and the run on repo (2012) — link
  45. Deep neural networks algorithms for stochastic control problems on finite horizon: convergence analysis (2021)
  46. Deep learning approximation for stochastic control problems (2016) — link
  47. Recent developments in machine learning methods for stochastic control and games (2024) — link
  48. ILLIQUIDITY COMPONENT OF CREDIT RISK – THE 2015 LAWRENCE R. KLEIN LECTURE (2016) — link
  49. Strategic Complementarity, Fragility, and Regulation (2014) — link
  50. Coordination Failures and the Lender of Last Resort: Was Bagehot Right After All? (2004) — link
  51. Two centuries of systemic bank runs (2024) — link
  52. Deal for failed Silicon Valley carries record estimated cost to FDIC at $20B (2023) — link
  53. Does One Soros Make a Difference? A Theory of Currency Crises with Large and Small Traders (2004) — link
  54. Public Information, Private Information, and the Multiplicity of Equilibria in Coordination Games (2002) — link
  55. A General Theory of Equilibrium Selection in Games (1988) — link
  56. Machine-learning a family of solutions to an optimal pension investment problem (2025) — link
  57. Application of data clustering and machine learning in variable annuity valuation (2013) — link
  58. A data-driven neural network approach to optimal asset allocation for target based defined contribution pension plans (2019) — link
  59. A hybrid deep learning method for optimal insurance strategies: Algorithms and convergence analysis (2021) — link
  60. Bayesian CART models for insurance claims frequency — → 2303.01923
  61. Machine learning for retirement planning (2020)
  62. Heterogeneous Retirement Savings Strategy Selection with Reinforcement Learning (2023)
  63. A neural network approach to efficient valuation of large portfolios of variable annuities (2016) — link
  64. Handbook of Convergence Theorems for (Stochastic) Gradient Methods (2024) — link
  65. Risk aversion with many commodities (1974) — link
  66. Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework (1989) — link
  67. Efficient Per-Example Gradient Computations (2015) — link
  68. Tutorial on amortized optimization (2023)
  69. Deep hedging: continuous reinforcement learning for hedging of general portfolios across multiple risk aversions (2022) — link
  70. GradNorm : gradient normalization for adaptive loss balancing in deep multitask networks (2018)
  71. Learning values across many orders of magnitude (2016)
  72. A Hybrid Deep Reinforcement Learning Method for Insurance Portfolio Management (2026) — link
  73. Monte Carlo Methods in Financial Engineering (2004)

2 of 81 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.