Optimal life insurance and annuity decision under money illusion

ArXiv ID: 2410.20128 “View on arXiv”

Authors: Unknown

Abstract

This paper investigates the optimal consumption, investment, and life insurance/annuity decisions for a family in an inflationary economy under money illusion. The family can invest in a financial market that consists of nominal bonds, inflation-linked bonds, and a stock index. The breadwinner can also purchase life insurance or annuities that are available continuously. The family’s objective is to maximize the expected utility of a mixture of nominal and real consumption, as they partially overlook inflation and tend to think in terms of nominal rather than real monetary values. We formulate this life-cycle problem as a random horizon utility maximization problem and derive the optimal strategy. We calibrate our model to the U.S. data and demonstrate that money illusion increases life insurance demand for young adults and reduces annuity demand for retirees. Our findings indicate that the money illusion contributes to the annuity puzzle and highlights the role of financial literacy in an inflationary environment.

Keywords: Life-Cycle Model, Money Illusion, Life Insurance, Annuities, Inflation, Multi-Asset

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced stochastic calculus (Ornstein-Uhlenbeck processes, HJB equations) to model optimal life-cycle decisions, indicating high mathematical complexity. It is also empirically rigorous, as it calibrates the model to U.S. data and conducts numerical simulations to derive economic insights, though it lacks live backtesting or open-source code.

  flowchart TD
    A["Research Goal"] -->|Formulate life-cycle model| B["Methodology"]
    B --> C["Define objective: Maximize expected utility<br>under money illusion"]
    C --> D["Model assets: Nominal bonds,<br>inflation-linked bonds, stock"]
    D --> E["Include life insurance<br>and annuity decisions"]
    E --> F["Data Inputs"]
    F -->|U.S. economic data| G["Calibrate model parameters"]
    G -->|Optimization algorithm| H["Key Findings / Outcomes"]
    H -->|Money illusion increases| I["Higher life insurance demand for young adults"]
    H -->|Money illusion reduces| J["Lower annuity demand for retirees"]
    J -->|Explains| K["Contributes to annuity puzzle"]