On the control of defined-benefit pension plans

We extend previous work in two ways. First, we introduce a model for short-term interest rates, which can be used to help control contribution-rate volatility. Second, we model three assets rather than the usual one (cash, bonds and equities) to allow comparison of different asset strategies. We develop formulae for unconditional means and variances. We then discuss how variability can be controlled most efficiently by setting contribution rates with reference to current funding levels and interest rates.