Investment Policies for Defined-Contribution Pension Funds

Dynamic optimal investment policies are derived for a defined-contribution pension plan under expected utility maximization and under minimization of the shortfall probability. It is assumed that
the return attributed by the fund on the accrued retirement benefits of employees may depend on the funding ratio and partly on the investment performance of the fund. The resulting investment policies
are compared with the reference case where the attributed return is assumed to be constant. Under expected utility maximization the investment strategy becomes more aggressive than in the reference
case if the attributed return increases with the funding ratio. Higher net contributions lead to a more aggressive investment strategy. However, participation of employees in the investment performance
of the fund has an ambiguous effect on the investment policy. Under expected utility maximization the funding ratio is lognormally distributed and asymptotically well behaved. For the minimization
of the shortfall probability a technique developed by Pestien and Sudderth (1985) is used. Formulas for the shortfall probability are derived and discussed.