Optimal pension decision under heterogeneous health statuses and bequest motives

Abstract

In this paper, we study the optimal decision between ELA(Equity Linked Annuity) and ELID(Equity Linked Income Drawdown) pension plans under heterogeneous personal health statuses and bequest motives. In the ELA pension plan, the survival member receives the mortality credit, and leaves no bequest at the time of death, while the member receives no mortality credit and receives the fund wealth as bequest at the time of death in the ELID pension plan. The pension member controls the asset allocation and benefit outgo policies to achieve the objectives. We explore the square deviations between the actual benefit outgo and the pre-set target, and the square and negative linear deviations between the actual bequest and the pre-set target as the disutility function. The minimization of the disutility function is the objective of the stochastic optimal control problem. Using HJB (Hamilton-Jacobi-Bellman) equations and variational inequality methods, the closed-form optimal policies of the ELA and ELID pension plans are derived. Furthermore, the optimal decision boundary between the ELA and ELID plans is established. It is the first time to study the impacts of heterogeneous personal health status and bequest motive on the optimal choice between the ELA and ELID pension plans under the original performance criterions. The worse health status and higher bequest motive result in the higher utility of the ELID pension plan, and vice versa. The worse heath status increases the proportion allocated in the risky asset and increases the benefit outgo in both pension plans. The bequest motive has positive impacts on the proportion in the risky asset and negative impacts on the benefit outgo in the ELID pension plan.