Optimal investment strategies of a defined Contribution pension fund

Abstract

The issue that a pension fund manager faces is how to optimize his/her investment strategies. The question we solve is the optimal design of the minimum guarantee in a defined contribution pension Fund Scheme. We study the optimal asset allocation strategy a given fund manager can adopt to maximize surplus (the difference between the pension fund and the Guarantee) and the payback ratio (ratio between total wealth and Guarantee). Finally, we analyze the impact of the main parameter which is the sharing rule between the contributor and the pension fund. The sharing rule is a way to creating a continuum between two extreme pension funding methods that are Defined Contribution and Defined Benefit pension fund, and the sharing rule allows partial risk transfer between the contributors and the pension fund manager. We consider a case of a pension fund company which invests in a bond, stocks and a money market account. The uncertainty in the financial market is driven by Brownian motions. Numerical simulations will be performed to compare the different models.