  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.
