The Life Care Annuity: enhancing product features and refining pricing methods

ArXiv ID: 2404.02858 “View on arXiv”

Authors: Unknown

Abstract

The state-of-the-art proposes Life Care Annuities, that have been recently designed as variable annuity contracts with Long-Term Care payouts and Guaranteed Lifelong Withdrawal Benefits. In this paper, we propose more general features for these insurance products and refine their pricing methods. We name our proposed product GLWB-LTC''. In particular, as to the product features, we allow dynamic withdrawal strategies, including the surrender option. Furthermore, we consider stochastic interest rates, described by a Cox-Ingersoll-Ross process. As to the numerical methods, we solve the stochastic control problem involved by the selection of the optimal withdrawal strategy through a robust tree method, which outperforms the Monte Carlo approach. We name this method Tree-LTC’’, and we use it to estimate the fair price of the product, as some relevant parameters vary, such as, for instance, the entry age of the policyholder. Furthermore, our numerical results show how the optimal withdrawal strategy varies over time with the health status of the policyholder. Our findings stress the important advantage of flexible withdrawal strategies in relation to insurance policies offering protection from health risks. Indeed, the policyholder is given more choice about how much to save for protection from the possible disability states at future times.

Keywords: Life Care Annuities, Stochastic Control, Cox-Ingersoll-Ross Process, Optimal Withdrawal Strategy, Long-Term Care, Insurance

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper employs advanced stochastic calculus (Cox-Ingersoll-Ross interest rates, American option pricing via tree methods) which demands high mathematical sophistication, but the empirical component is limited to theoretical pricing model comparisons and sensitivity analysis without backtests on historical financial data.

  flowchart TD
    A["Research Goal:<br>Enhance Life Care Annuities & Refine Pricing"] --> B["Modeling Framework<br>Cox-Ingersoll-Ross for interest rates"]
    B --> C["Stochastic Control Problem<br>Optimizing withdrawal strategy"]
    C --> D{"Numerical Method"}
    D -- Traditional --> E["Monte Carlo Approach"]
    D -- Proposed --> F["Tree-LTC Method<br>(Robust Tree)"]
    E --> G["Analysis & Pricing"]
    F --> G
    G --> H["Key Findings<br>Optimal strategy varies by health status<br>Flexible withdrawals are advantageous"]
    
    style A fill:#f9f,stroke:#333,stroke-width:2px
    style H fill:#bbf,stroke:#333,stroke-width:2px