Multi-state Health-contingent Mortality Pooling: A Heterogeneous, Actuarially Fair, and Self-sustaining Product

Yuxin Zhou and Jan Dhaene

Abstract: There is a growing need for higher retirement incomes to cover the higher long-term care (LTC) costs when retirees become functionally disabled or ill. However, most of the existing mortality pooling products in the literature do not consider the health status of members. Hence, they do not provide higher retirement incomes to members who have LTC needs due to deteriorated health conditions. To address this issue, we propose a health contingent mortality pooling product that is actuarially fair and self-sustaining, featuring health-state-dependent income payments. The proposed framework allows free transitions between health states so that recovery from functional disability is allowed. The framework has the flexibility to allow any number of health states, while we use a five-state model with the health states constructed from two dimensions, which are functional disability and morbidity. Moreover, the product allows heterogeneity so members can have different ages, contributions, initial health states, joining times, and rates of investment returns. Allowing heterogeneous members to join helps increase the pool size and generate more stable income payments. We find that the proposed health-contingent pooling product consistently provides significantly higher retirement incomes to members with functional disability and morbidity, while the costs to healthy members are relatively low. We also find that the jump in income payments happens immediately when there is a transition to a less healthy state, allowing members to quickly obtain higher incomes to cover the higher costs incurred by being functionally disabled or ill. Meanwhile, if the member recovers from functional disability, the income payments will decrease to reflect the reduced LTC cost.

Keywords: Mortality pooling product, Long-term care, Retirement income, Health-contingent, Multi-state health model