Mean-variance portfolio selection and efficient frontier for defined contribution pension schemes

We solve a mean-variance portfolio selection problem in the accumulation phase of a defined contribution pension scheme. The efficient frontier, which is found for the 2 asset case as well as the $n+1$ asset case, gives the member the possibility to decide his own risk/reward profile. The mean-variance approach is then compared to other investment strategies adopted in DC pension schemes, namely the target-based approach and the lifestyle strategy. The comparison is done both in a theoretical framework and based on simulations. As a result, it turns out that the target-based approach can be formulated as a mean-variance optimization problem, and therefore the corresponding mean and variance of the final fund belong to the efficient frontier; on the other hand, the lifestyle strategy seems to be very far from being efficient in the mean-variance setting.