Abstract:
This paper discusses the modelling and control of pension funds. A contino us-time stochastic
pension fund model is proposed in which there are n risky assets plus the risk-free asset as well
as randomness in the level of benefit outgo. We consider Markov control strategies which
optimise over the contribution rate and over the range of possible asset-allocation strategies.
For a general (not necessarily quadratic) loss function it is shown that the optimal proportions of
the fund invested in each of the risky assets remain constant relative to one another.
Furthermore, the asset allocation strategy always lies on the capital market line familiar from
modem portfolio theory.
A general quadratic loss function is proposed which provides an axplicit solution for the optimal
contribution and asset-allocation strategies. It is noted that these solutions are not dependent on
the level of uncertainty in the level of benefit outgo, suggesting that small schcmes should
operate in the same way as large ones. The optimal asset-allocation strategy, however, is found
to be counterintuitive leading to some discussion of the form of the loss function.
The stationary distribution of the process is considered and optimal strategies compared with
dynamic control strategies.
Finally there is some discussion of the effects of constraints on contribution and asset allocation
strategies.
