Joint Life Long-Term Care Insurance: A Semi-Markov Multi-State Model Integrating LTC Prevalence and Mortality Trends - Roro Anteng; Adhitya Ronnie Effendie (Jambura Journal of Mathematics, 2025)
This study develops a two-person joint-life long-term care (LTC) insurance pricing framework for married couples by incorporating mortality and LTC risks within a semi-Markov-inspired multi-state model. The transition intensity structure accounts for Gompertz mortality, potential common-shock events, and a duration-dependent bereavement effect. LTC-related transition intensities are adjusted using proportional factors, while the transition probabilities are approximated using a matrix-exponential procedure and applied to the calculation of net single premiums.A numerical case study is presented for a married couple aged 62 and 60 under a 20-year coverage period. The alternative benefit designs include mortality protection, LTC annuity protection, and a combined design integrating death and LTC benefits. The results indicate mortality dependence between spouses through the common-shock and post-bereavement mechanisms and show that broader benefit coverage produces a higher net single premium.The main contribution of this study is an actuarial pricing framework for two associated individuals that jointly incorporates spousal mortality dependence, LTC incidence, and combined death and LTC benefits in a unified multi-state structure.