PENSION FUNDING WITH TIME DELAYS AND AUTOREGRESSIVE RATES OF INVESTMENT RETURN

We consider pension funding methods which determine contributions at each valuation by spreading the unfunded liability over a fixed number of years. Real rates of return on the assets are assumed to be represented by a first-order autoregressive process. The contribution rate is fixed relative to the fund level but with a time delay. This means that the fund level and contribution rate have the structure of a non-linear time series, where an autoregressive component is multiplied by the autoregressive rate of return. Recursive formulae are obtained for the expectations and the variability of fund and contribution levels for finite t. Under certain conditions, these moments converge in time to limits which, although not explicitly obtainable, can nevertheless be found by a numerical procedure in any given case.