Paper: arXiv 2506.02155

Authors: Bushra Shehnam Ashraf, Thomas S. Salisbury

Abstract

We study optimal consumption and retirement using a Cobb-Douglas utility and a simple model in which an interesting bifurcation arises. With high wealth, individuals plan to retire. With low wealth they plan to never retire. At a critical level of initial wealth they may choose to defer this decision, leading to a continuum of wealth trajectories with identical utilities.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper features dense mathematical derivations including HJB equations, ODEs, and free boundary problems, placing it in the high math range. It includes numerical implementation details (Matlab, finite-difference schemes) and calibration based on real-world data, indicating substantial empirical work, though not full backtesting.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>How does initial wealth affect<br>optimal retirement decisions?"] --> B["Methodology:<br>Cobb-Douglas Utility &<br>Dynamic Programming"]
  B --> C["Data/Inputs:<br>Initial Wealth Levels<br>High vs. Low vs. Critical"]
  C --> D["Computational Process:<br>Optimize Consumption & Retirement<br>under HJB Constraints"]
  D --> E{"Outcome Analysis"}
  E --> F["Findings: Bifurcation Behavior"]
  F --> G["High Wealth → Retire Early"]
  F --> H["Low Wealth → Never Retire"]
  F --> I["Critical Wealth →<br>Indeterminate/Continuum of Paths"]