Care-dependent target benefit pension plan with minimum liability gap

With the progressive aging of populations, the significance of long-term care (LTC) services in aging societies is growing. In this paper, we integrate LTC services with pensions, studying a stochastic model for a care-dependent target benefit pension (TBP) plan. The plan members' target benefit rates are set according to the care cost for three different health states, i.e., healthy, mildly disabled and severely disabled states. The pension liability evaluation is defined as the potential compensation to all active and retired members, under the assumption of the pension fund default. The objective of minimizing the benefit gap and liability gap is achieved by addressing a stochastic optimal control problem. Then, we derive analytic solutions for optimal investment and benefit payment strategies by employing the corresponding Hamilton-Jacobi-Bellman (HJB) equation. Numerical results show that under a fixed aggregate contribution of the care-dependent TBP, a slight decrease in the target benefit for healthy retirees leads to a significant increase for retirees in both mildly and severely disabled states, thereby improving equity for disabled retirees. Furthermore, we compare the care-dependent TBP with a traditional TBP and a care-dependent tontine in terms of risk sharing, financial stability, and intergenerational equity, highlighting the advantages of the care-dependent TBP.