Care-Dependent Tontines

With the gradual deepening of aging, the medical and pension problems of the half-disabled and disabled elderly will become increasingly prominent. Policymakers, academics, and the public at large shed extensive concerns about the cost of aging societies. Although long-term care (LTC) insurance comes up as one of the solutions, private LTC does not perform well in the market. The combination of tontines with long-term care contingency stands out as an alternative to attract participants. In this article, we propose two ways of designing the care-dependent tontines: (i) all the insured members are considered to be in one pool; (ii) at each time t, we allocate them into two groups: the healthy and the severely sick. We find out the optimal payment structures of the care-dependent tontine as well as the care-dependent annuity that maximize the policyholder’s expected lifetime utility. Based on data from China Health and Retirement Longitudinal Study (CHARLS), we theoretically and numerically compare the different care-dependent products in consideration with an actuarially fair premium. Results imply that the care-dependent annuity is the most attractive one. However, when we take account of the risk charges to further compare the products, we find that both care-dependent tontines present as better choices of policyholders in comparison with care-dependent annuities. Moreover, two-pool care-dependent tontines draw attractions to the policyholder with a smaller risk aversion coefficient, while one-pool care-dependent tontines are more appealing to the more risk-averse policyholders.