Optimal investment strategies and intergenerational risk sharing for target benefit pension plans

In this paper, we consider a stochastic model for a target benefit pension fund in continuous time, where the plan members' contributions are set in advance while the pension payments depend on the financial situation of the plan, with risk sharing between different generations. The pension fund is invested in both a risk-free asset and a risky asset. In particular, stochastic salary rates and the correlation between salary movements and financial market fluctuations are considered. Using the stochastic optimal control approach, we derive closed-form solutions for optimal investment strategies as well as optimal benefit payment adjustments, which minimize the combination of benefit risk (in terms of deviating from the target) and intergenerational transfers. Numerical analysis is presented to illustrate the sensitivity of the optimal strategies to parameters of the financial market and salary rates. We also consider how the optimal benefit changes with respect to different target levels.