AUTOREGRESSIVE RATES OF RETURN AND THE VARIABILITY OF PENSION CONTRIBUTIONS AND FUND LEVELS FOR A DEFINED BENEFIT PENSION SCHEME

A mathematical model is described which facilitates the comparison of different pension funding methods. Real investment rates of return on the pension fund are assumed to be represented by an autoregressive model for the corresponding force of interest. Expressions for the moments of the contribution rate and fund level are then derived. This leads to a discussion of methods of funding which are optimal in the sense of the period for spreading surpluses and dificiencies which should be chosen in order to reduce the variability of both contributions and fund levels.