Optimal dynamic control for the defined benefit pension plans with stochastic benefit outgo

This work is devoted to a continuous time dynamic pension funding model in a defined benefit plan of an employment system. We extend the analysis of some standard models by incorporating a source of uncertainty in the benefit outgo. The key assumption is that the random benefits increase on average at an exponential rate. We model the preference of the manager with the main objective of minimizing both the contribution rate risk and the solvency risk. Two different situations are studied regarding the investment decisions. In the first case, the fund is invested at a constant, risk-free rate of interests; in the second case, the promoter invests in a portfolio with a risky asset and a risk-free bond. We provide, in both cases, explicit expressions for the actuarial liability, normal costs, value function, and the supplementary contribution rate.