Optimal investment and benefit adjustment problem for a target benefit pension plan with Cobb-Douglas utility and Epstein-Zin recursive utility

This paper studies an optimal investment and benefit adjustment problem for a target benefit pension plan. The pension sponsor can adjust the benefit level to guarantee the stable operation of the plan. The pension is allowed to invest in a risk-free bond and a stock. The weighted product of the benefit outgo and pension wealth is considered in the objective function, which is taken in the form of Cobb-Douglas utility. Thus the plan takes both the benefit level and terminal wealth of the pension into account and then the benefit payment are dependent on the financial situation of the plan. By applying dynamic programming approach, we establish the corresponding Hamilton-Jacobi-Bellman equation and derive the optimal investment-benefit strategy and the value function explicitly. The verification theorem is presented and proved. Furthermore, the recursive utility is considered as an extension and we find that the elasticity of intertemporal substitution has a positive effect on the optimal benefit level. Finally, numerical examples are given and demonstrate that this pension scheme is sustainable and can provide stable and consecutive incremental benefit payment for future generations.(c) 2021 Elsevier B.V. All rights reserved.