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

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 to the financial market and is allowed to invest in a risk-free asset and a risky asset. The plan manager aims to find optimal investment strategies and optimal intergenerational risk-sharing arrangements by minimizing the unstable contribution risk, the unstable benefit risk and the discontinuity risk under the worst-case scenario. By applying the stochastic optimal control approach, robust optimal strategies are derived under the worst-case scenario for 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 reasonable way to alleviate the stress of the aging problem.