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

Longevity risk has become increasingly significant in actuarial and financial applications due to improvements in life expectancy and demographic changes. The uncertainty of future mortality trends motivates the use of stochastic mortality models to capture mortality randomness. Building on the foundational Lee−Carter (LC) model and a recent Fourier-based extension for modelling time-varying age patterns, this study proposes an enhanced LC−Fourier model tailored to Malaysian mortality dynamics. Mortality data disaggregated by age and gender from 1980 to 2023 were obtained from the Department of Statistics Malaysia (DOSM). The proposed model decomposes the age-sensitivity parameter of the LC model into a Fourier series of three sinusoidal components with time-varying amplitude and phase parameters. This flexible structure reflects the presence of two splitting ages and three peak-age effects, enabling the model to capture multiple age-specific mortality patterns observed in the Malaysian population. Model performance for both the LC and LC−Fourier frameworks is evaluated using the Mean Absolute Percentage Error (MAPE) for fitted mortality rates and life expectancy at birth across male and female groups. Empirical results demonstrate that the two-split, three-peak LC−Fourier model achieves a superior fit and yields improved mortality projections compared with the baseline LC model, particularly at older ages. The enhancements are most notable for females. These findings highlight the model’s ability to capture structural changes in age-dependent mortality patterns that are not adequately represented by the original LC model.