Dynamic optimal adjustment policies of hybrid pension plans

Abstract

In this paper, we propose two methods to dynamically adjust the contribution rate and the benefit rate of the hybrid pension fund: the semi-transparent case and the transparent case. The adjustment coefficients (time-varying or constant) and the asset allocation policy are controlled to minimize the disutility of the adjustment risk and the unsustainable risk. The adjustment rates are proportional to the unfunded liability (gap) of the hybrid pension fund, and the gap is estimated by the dynamically updated contribution and benefit rates. This forms the nested structure of the optimization problem, which could be solved based on a multi-dimensional stochastic control problem. The results show that the optimal policy adjusts the contribution and the benefit rates fairly among the cohorts and reduces the terminal fund gap effectively in the two cases. Comparing with the semi-transparent case, the adjustment risk is more undertaken by the current participants and the pension rules are more stable after a long time in the transparent case.