Mortality Modeling: From Static Numbers to Dynamic Prediction

In the past, actuarial science applied current mortality statistics (static life tables) directly to the future. However, human lifespans are continuously increasing alongside medical advances. Modern actuarial science focuses on modeling this trend of mortality improvement.

1. Static vs. Dynamic Models

• Static Model: “The probability of a 60-year-old dying this year is 2%.” (Fixed current observations)
• Dynamic Model: “The probability of a 60-year-old dying this year is 2%, but it is trending downward by 1% annually.” (Reflecting changes over time)

2. Structure of the Lee-Carter Model

Published in 1992, the Lee-Carter model has become the standard for mortality forecasting.

$\ln(m_{x,t}) = \alpha_x + \beta_x \kappa_t + \epsilon_{x,t}$

• $\alpha_x$: Average mortality level at each age.
• $\kappa_t$: General change in mortality over time (the trend).
• $\beta_x$: Sensitivity of a specific age group to the overall trend ($\kappa_t$).

3. Aging and Longevity Risk

While living longer is a blessing for individuals, it represents a significant risk for insurance companies and pension funds that must provide benefits over longer periods.

💡 Professor’s Tip

Mortality modeling is more than just math; it’s a tool for diagnosing social structures. Recently, there has been active research in stochastic modeling to understand how unexpected events like climate change or pandemics “shock” future mortality trends.

🔗 Next Step

• Ch7: Basics of Non-Life Actuarial Mathematics