Pension funding incorporating downside risks

This research extends Haberman and Sung’s [Insurance: Mathematics and Economics 15 (1994) 151] and Chang’s [Insurance: Mathematics and Economics 24 (1999) 187] works to study optimal funding strategies through the control mechanism. The paper further generalizes the previous research in three ways. First, downside risks, under-funding risk and over-contributing risk, are included additionally in the risk minimization criterion to obtain the optimal solutions. Second, we allow the weighting factors in the performance criterion to belong to a broader parametric family. Third, the rates of investment returns are assumed to follow the auto-regressive process. The above three generalization indeed include traditional model as special cases. Furthermore, an actual case is employed to investigate their financial impacts on funding and contribution due to our generalization. The results show that neglecting to recognize the under-funding risk and the over-contribution risk will lead to a significant difference in optimal funding schedule. The weighting factors and the returns of investment also play critical roles in obtaining the optimal strategy.