Betty Frankl: Mortality Forecasting: A Comparison of the Lee-Carter Model and the Plat Model for Swedish Female Data in Insurance Applications

Abstract: Accurate mortality forecasting is central to life insurance pricing and reserving, since premiums and reserves depend directly on projected mortality rates. This thesis compares two stochastic mortality models: the classical Lee-Carter model, and the newer Plat model, which additionally includes a cohort effect.

The models are fitted to Swedish female mortality data from the Human Mortality Database for ages 20–100 and years 1860–2024, using a Poisson regression framework, with the final 20% of the years held out for out of sample evaluation. Three forecasting approaches are considered for the time dependent parameters. The first is an ARIMA model, with order selected via AIC, BIC, and cross validation. The second is a random walk with drift. The third restricts the fitted age range to 20–89, forecasting these ages using a random walk with drift, while mortality for ages 90–100 is assumed constant over time. To evaluate the models further in a practical application, we also study the out of sample errors for the total expected benefit for both annuity and term insurance contracts.

The Plat model generally produces more accurate predictions, particularly with the random walk forecasting approach, with an out of sample deviance of approximately 16 versus 24–26 for most other models. The Lee-Carter model noticeably underestimates annuity benefits and overestimates term insurance benefits, which could lead to unfavorable financial outcomes for an insurer. However, in general Lee-Carter produces narrower prediction intervals than Plat. Therefore, we cannot conclude with certainty that Plat is superior overall.

The report may soon be available at kurser.math.su.se/mod/folder/view.php?id=13969