A Two-Split, Three-Peak Fourier Extension of the Lee–Carter Mortality Model

Longevity risk has become increasingly important in actuarial and financial applications owing to rising life expectancy and demographic change. To address uncertainty in future mortality trends, particularly age-specific variations, this study proposes a Fourier extension of the Lee–Carter (LC) mortality model for modeling Malaysian mortality dynamics. Mortality data by age and sex from 1980 to 2023 were obtained from the Department of Statistics Malaysia. The proposed model represents the LC age-sensitivity parameter using a Fourier series comprising three sinusoidal components. This formulation incorporates two splitting ages and three peak-age effects, enabling the model to capture complex age-specific mortality patterns. Model performance was assessed against the standard LC model using the Mean Absolute Percentage Error (MAPE) and Root Mean Squared Error (RMSE) for mortality rates and life expectancy at birth. The results show that the proposed two-split, three-peak LC–Fourier model improves the fit of mortality rates, with the greatest improvement observed among males aged 16 to 45 years. The model also reduces the average MAPE and RMSE for life expectancy at birth, indicating improved forecasting accuracy. Overall, the findings demonstrate that the proposed model captures mortality patterns that are not adequately represented by the conventional LC framework.