Paper: arXiv 2407.15388

Authors: Xiaobai Zhu, Kenneth Q. Zhou, Zijia Wang

Abstract

The significance of mortality modeling extends across multiple research areas, ranging from life insurance valuation to optimal lifetime decision-making. Existing approaches, such as mortality laws and factor-based models, often fall short in capturing the complexity of individual mortality, hindering their ability to address specific research needs. To overcome these limitations, this paper introduces a novel approach to mortality modeling centered on the dynamics of individual vitality. A four-component framework is developed to account for initial conditions, natural aging processes, stochastic fluctuations, and accidental events over an individual’s lifetime. We demonstrate the framework’s analytical capabilities across various settings and explore its practical implications in solving life insurance problems and deriving optimal lifetime decisions. Our results show that the proposed framework not only encompasses existing mortality models but also provides individualized mortality outcomes and offers an intuitive explanation for survival biases.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 5.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a novel four-component vitality dynamics framework for mortality modeling, framing death as a stochastic first passage problem. It demonstrates strong mathematical rigor by unifying several existing actuarial models and providing analytical tractability for insurance valuation.

Research Flowchart

  flowchart TD
    A[Goal: Overcome limitations of existing mortality models] --> B[Develop Individual Vitality Framework]
    
    B --> C[Framework Inputs & Components: <br>Initial Vitality, Natural Aging, <br>Stochastic Fluctuations, Accidental Events]
    
    C --> D[Model Dynamics & Solve Stochastic Equations]
    
    D --> E[Apply to Life Insurance Valuation & <br>Optimal Lifetime Decision-Making]
    
    E --> F[Outcomes: Individualized mortality outcomes, <br>generalization of existing models, & <br>intuitive explanation of survival biases]

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