Relative Choice Models for Income Drawdown in a Defined Contribution Pension Scheme

Abstract

This paper extends a target-based model of income drawdown developed in Gerrard et al. (Insurance: Mathematics and Economics 35: 321–342 2006]) (GHV) for the distribution phase of a defined contribution pension scheme. The optimal investment strategy of the pension fund and the optimal drawdown are found using linear-quadratic optimization, which minimizes the deviation of the fund and the drawdown from prescribed targets. The GHV model is modified by nondimensionalizing the loss function, so that there is a relative choice between outcomes.

Using this model, three classes of target are studied. Endogenous deterministic targets are suggested from the form of the optimal controls, while exogenous deterministic targets can be stated without knowledge of the optimization problem. The third class of stochastic targets is similar to recent annuity products, which incorporate investment risk. Each scheme represents a trade-off between investment risk and return, and this is illustrated by numerical simulation with reference to a canonical example. A particularly attractive form of income drawdown is given by an implied rate of return target. This yields a reasonable investment strategy and a robust consumption profile with age. In addition, it can be easily explained to pension scheme members.