Contribution and solvency risk in a defined benefit pension scheme

This paper presents a stochastic investment model for a defined benefit pension scheme, in the presence of IID real rates of return. The spread method of adjustment to the normal cost is used to deal with surpluses or deficiencies. Two types of risk are identified, the “contribution rate risk” and the “solvency risk” which are concerned with the stability of the contributions and the security of the pension fund, respectively. A performance criterion is introduced to deal with the simultaneous minimisation of these two risks, using the fraction of the unfunded liability paid off (k) or the spread period (M) as the control variable. A full numerical investigation of the optimal values of k and M is provided. The results lead to practical conclusions about the optimal funding strategy and, hence, about the optimal choice of the contribution rate subject to the constraints needed for the convergence of the performance criterion.