Stochastic optimal control of annuity contracts

The purpose of this paper is to show how stochastic optimal control theory can be applied to find an optimal investment policy before and after retirement in a defined contribution pension plan where benefits are paid under the form of annuities; annuities are supposed to be guaranteed during a certain fixed period of time. Using different kinds of utility functions we try to look at different strategies on the one hand in the investment part (i.e. before retirement) and on the other hand in the payment part (i.e. after retirement). The needed change of strategy after retirement can be interpreted in this model as a typical ALM constraint taking into account a guaranteed technical interest rate used by the insurer.