Stochastic Multi-State Modeling for Critical Illness Insurance With Integration of Non-Homogeneous Trends and Pandemic Shocks

Abstract

This study develops a stochastic pricing framework for critical illness insurance using Indonesian population data. The framework captures the joint effects of mortality, morbidity, and longevity across age and sex. A multi-state model is constructed to represent transitions between one healthy state, eleven critical illness states, and death. Benefits are payable upon the first occurrence of a critical illness, upon death, and upon survival to age 95. Using publicly available incidence, prevalence, and mortality data, transition intensities are derived and projected to reflect future health risk patterns. Particular attention is given to the construction of transition intensities for first-time critical illness events under limited data availability. Pandemic-related mortality distortions are addressed through adjustment procedures, and the age domain is segmented to accommodate non-homogeneous mortality trends. Projection models are selected from seven stochastic mortality models based on performance criteria, and additional noise smoothing is applied when cohort-based models produce unstable projections. The results show that total expected costs for males and females are generally comparable. However, differences remain across age groups and benefit components. These findings support the use of age- and sex-specific pricing structures in critical illness insurance.