The thesis describes a dynamic programming approach to pension funding for a defined benefit pension scheme. The primary purpose of the thesis is to search for a pension funding plan balancing optimally the conflicting interests of the sponsoring employer and the trustees. The starting point of this problem is to mtroduce and define mathematically two types of risk concerned respectively with the stability and security of pension funding: the "solvency risk" and the "contribution rate risk". Next, two distinct linear asset/liability dynamic models are presented, based on specified assumptions: the "modified solvency-level growth equation" and the "zero-input, 100%-target solvency-level growth equation". We then consider the situation of a short-term, winding-up valuation with contribution rates unconstrained by any funding plan, and introduce three distinct finite-horizon control optimisation problems- deterministic, stochastic with complete state information and stochastic with incomplete state information. We then consider the situation of a long-term, going-concern valuation with contribution rates constrained by the spread funding plan, and introduce four distinct infinite-horizon deterministic control optimisation problems - stationary, quasi-stationary, non-stationary and threshold. The thesis derives optimal funding control procedures for the contribution rate by solving each of these seven control problems by means of the optimal control theory of dynamic programming.