Pricing for longevity risk in long-term care insurance

The increase in life expectancy due to improved health conditions in recent years has led to the longevity risk. This situation has caused an increase in the demand for health insurance over time, and the importance of long-term care insurance for older people which is designed to cover the long-term care needs has increased. In this study, longevity risk is investigated for the long-term care insurance with classified degrees of dependency. The long-term care insurance model is constructed by using Monte Carlo Simulation method according to two different scenarios: static structure in which the mortality rate does not change over time and dynamic structure in which the mortality rate changes depending on the increasing future life expectancy. The duration of dependency for long-term care insurance is modeled under the Weibull distribution of the semi-Markov process, which is explained by the Cox proportional hazard model and the frailty model. Probabilities of death and transition from a healthy state to a need of care state (dependent) are used from Turkey and France. Under the dependency structure, premiums for long-term care insurance and the reserve required to be allocated are calculated and the change in premiums with the effect of dependency is examined and it is concluded that the longevity risk caused more liability to the insurer.