Pension Funding with Moving Average Rates of Return

In the context of the model of pension funding introduced by Dufresne in 1986, explicit expressions are found for the first two moments of fund level and total contributions, when (1) actuarial gains and losses are amortized over N years, and (2) arithmetic rates of return on assets form a moving average process. The results are obtained via a Markovian representation for the bilinear process obtained for the actuarial losses. One conclusion is that the dependence between successive rates of return may have very significant effects on the financial results obtained.