Optimal retirement in presence of stochastic labor income: a free boundary approach in an incomplete market

Paper: arXiv 2407.19190

Abstract

In this work, we address the optimal retirement problem in the presence of a stochastic wage, formulated as a free boundary problem. Specifically, we explore an incomplete market setting where the wage cannot be perfectly hedged through investments in the risk-free and risky assets that characterize the financial market.

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 1.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper employs advanced mathematical techniques including stochastic control, free boundary problems, and duality transformations with extensive formal derivations and PDE analysis, but focuses entirely on theoretical modeling with no empirical data, backtests, or implementation details.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Optimal retirement with stochastic wage in incomplete market"] --> B["Methodology<br>Free Boundary Approach"]
  B --> C["Data/Input<br>Stochastic wage process & financial assets"]
  C --> D["Computation<br>Hamilton-Jacobi-Bellman & free boundary solution"]
  D --> E["Key Findings<br>Optimal retirement threshold & portfolio allocation"]