Optimal Control Approach to Spread Pension Funding When Rates of Return are Non-Stationary

After Benjamin(1984) introduced first the concept of control approach in the field of actuarial pension funding, this approach has been developed and is recently even more attracting the interests of actuarial professionals, in particular in the area of insurance premium pricing and pension contribution pricing. In the light of optimal control theory, we follow up the earlier works of Haberman and Sung (1994, 2002) who introduced a dynamic approach to pension funding, based on a linear dynamic system with a quadratic optimisation criterion (so-called LQP control problem). We consider funding plans, on a long-term and going-concern valuation base, for a defined benefit pension scheme where the spread method is used to eliminate actuarial valuation surpluses and deficiencies. We formulate the non-stationary LQP optimisation problem over infinite control horizon and note that it is insoluble. We propose an approximate optimisation procedure for solving the problem and illustrate this with a specific numerical example. Furthermore, we hope that this paper will contribute to bridging the gap between actuarial practices in the area of pension funding and optimal control theory in the area of engineering, which would enable the pension profession to analyse more systematically the financial structure of the pension scheme and also make further applied research on issues related to pension funding (including insurance premium pricing). So far, Korean actuarial profession have not much interest in this kind of optimal spread amortisation approach. But implementing the occupational pension scheme by the Korea labour law next year, the kind of approach would be one of main concerns in the field of setting up corporate capital structure, because the pension cost will affect the corporate cash flows and then the firms value.