Optimal investment problem for a hybrid pension with intergenerational risk-sharing and longevity trend under model uncertainty

Abstract

This paper studies the optimal investment problem for a hybrid pension plan under model uncertainty, where both the contribution and the benefit are adjusted depending on the performance of the plan. Furthermore, an age and time-dependent force of mortality and a linear maximum age are considered to capture the longevity trend. Suppose that the plan manager is ambiguity averse and is allowed to invest in a risk-free asset and a stock. The plan manager aims to find optimal investment strategies and optimal intergenerational risk-sharing arrangements by minimizing the cost of unstable contribution risk, the cost of unstable benefit risk and discontinuity risk under the worst-case scenario. By applying the stochastic optimal control approach, closed-form solutions are derived under a penalized quadratic cost function. Through numerical analysis and three special cases, we find that the intergeneration risk-sharing is achieved in our collective hybrid pension plan effectively. And it also shows that when people live longer, postponing the retirement seems a feasible way to alleviate the stress of the aging problem.

An Equilibrium Strategy for Target Benefit Pension Plans with a Longevity Trend and Partial Information

“…On the other hand, as people age, the force of mortality increases. Inspired by Knell (2018) [31], who assumed that the maximum age of survival was an increasing function of time, Fu (2023) [33] also applied an age-and time-dependent mortality force, called the modified Makeham's Law, to describe the longevity risk.…”