Optimal Annuitization Time Under a Mortality Shock

Battle Count: 81

This paper is primarily focused on retirement planning and actuarial science rather than quantitative trading. While it uses geometric Brownian motion (common in financial modeling) and optimal stopping theory (relevant to American option pricing), the application domain is annuitization decisions for individuals, not trading strategies. The financial modeling techniques (GBM, exponential jump times, free boundary problems) have some transferable relevance to derivatives pricing and portfolio optimization, but the core contribution is in insurance/retirement economics.

The paper involves solving multiple free-boundary problems across different parameter regimes (K<0, K>0, K=0) and health states. The analytical solutions require careful case analysis with nonlinear equations for threshold determination. The numerical implementation requires Monte Carlo simulation of wealth paths with exponential jump times, solving ODEs via variation of parameters, and handling multiple interacting parameters. The supplementary proofs involve complex integral computations with Gaussian CDFs and characteristic exponents.

The paper provides explicit closed-form analytical solutions for all parameter configurations, detailed parameter calibration from public data (Human Mortality Database, S&P500, T-bill data), and a complete supplementary material with proofs. All model parameters are clearly stated in Table 1. However, no code repository is provided for the numerical simulations.