Optimal investment of DC pension plan based on a weighted utility

We investigate the DC pension manager's portfolio problem when he bases decisions on both absolute level of total wealth and comparisons to a certain pre-defined reference point. This setting leads to a non-concave objective utility and therefore a non-concave utility maximization problem. We apply the concavification technique to solve the non-concave optimization problem and obtain the closed-form representations of the optimal wealth process and the optimal strategies. Numerical results show that if the manager pays much more attention to the change of wealth relative to the reference point, then he will take a more conservative investment strategy due to risk aversion over gains.