Paper: arXiv 2503.09377

Authors: Mei Choi Chiu, Ling Wang, Hoi Ying Wong

Abstract

Empirical studies with publicly available life tables identify long-range dependence (LRD) in national mortality data. Although the longevity market is supposed to benchmark against the national force of mortality, insurers are more concerned about the forces of mortality associated with their own portfolios than the national ones. Recent advances on mortality modeling make use of fractional Brownian motion (fBm) to capture LRD. A theoretically flexible approach even considers mixed fBm (mfBm). Using Volterra processes, we prove that the direct use of mfBm encounters the identification problem so that insurers hardly detect the LRD effect from their portfolios. Cointegration techniques can effectively bring the LRD information within the national force of mortality to the mortality models for insurers’ experienced portfolios. Under the open-loop equilibrium control framework, the explicit and unique equilibrium longevity hedging strategy is derived for cointegrated forces of mortality with LRD. Using the derived hedging strategy, our numerical examples show that the accuracy of estimating cointegration is crucial for hedging against the longevity exposure of insurers with LRD national force of mortality.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 4.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a sophisticated theoretical framework combining fractional Brownian motion, cointegration, Volterra processes, and BSDEs for time-consistent open-loop equilibrium control in longevity hedging. While the mathematical derivation and theoretical proof regarding mixed fBm identification are highly rigorous, the empirical component relies primarily on numerical simulations rather than extensive real-world portfolio backtesting.

Research Flowchart

  flowchart TD
    A[Research Goal: Model insurer mortality with Long-Range Dependence LRD & derive hedging strategy] --> B[Data Inputs: Publicly available national life tables & insurer portfolio data]
    
    B --> C[Theoretical Analysis: Prove identification problem of direct mixed fBm via Volterra processes]
    
    C --> D[Methodology: Apply Cointegration to transfer national LRD info to insurer mortality models]
    
    D --> E[Optimization: Derive explicit equilibrium longevity hedging strategy via open-loop equilibrium control]
    
    E --> F[Findings: Cointegration accuracy is crucial for hedging insurer longevity risk under national LRD]