Stochastic pension fund modelling

This paper considers the stochastic behaviour of the funding level of a defined benefit pension plan through time and its relationship with the plan contribution rate. First, we investigate the effect of the valuation basis and of the amortization period on the variability of funding levels and contribution rates and this introduces the concept of the efficient frontier as a means of choosing an optimal funding strategy. Second, we consider models with dependent rates of return and provide a sufficient condition for the funding level to be ergodic. Upon considering the AR(1) model we derive a recursive method for calculating the conditional distribution of the funding level and provide further insight into the main factors which influence the behaviour of the funding level.