Paper: arXiv 2606.03158

Authors: Steven Campbell, Agostino Capponi, Ananya Parashar

Abstract

We study optimal portfolio choice for a household managing two goals at once. A random-deadline precautionary goal, such as a medical emergency, must be paid in full whenever it arrives and is affordable; a fixed-deadline accumulation goal, such as a target retirement lifestyle, may be declined at its deadline. We show that precautionary saving crowds out growth-oriented investment, and deadline pressure is amplified by the competing precautionary claim. We characterize the value function as the unique viscosity solution of an HJB equation, and derive the household’s optimal terminal funding rule. The household funds the fixed-deadline goal exactly when the direct benefit at least offsets the resulting drop in the value of keeping the precautionary goal funded. We calibrate the model and find that both flexibility and fungibility are most valuable at intermediate wealth. Committing in advance to fund a goal sacrifices flexibility, while managing each goal in its own account sacrifices fungibility.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly mathematical framework using HJB equations and viscosity solutions to address a novel portfolio choice problem. While the empirical calibration is present, the core contribution is theoretical, demonstrating strong rigor in its mathematical derivations and economic insights.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimal Portfolio Choice with Competing Precautionary & Accumulation Goals] --> B{Methodology: Stochastic Optimal Control & HJB Equation};
    B --> C{Inputs: Household Preferences, Market Dynamics, Goal Parameters};
    C --> D[Computational Process: Solve HJB Equation for Value Function & Optimal Controls];
    D --> E[Key Findings: Precautionary Saving Crowds Out Growth Investment];
    E --> F[Key Findings: Deadline Pressure Amplified by Precautionary Claim];
    F --> G[Key Findings: Optimal Terminal Funding Rule & Value of Flexibility/Fungibility at Intermediate Wealth];