Griselda Deelstra, Martino Grasselli, Pierre-François Koehl
The question we solve is the optimal design of the minimum guarantee in a Defined Contribution Pension Fund Scheme.
We endogeneize the investment in the financial market by assuming that the pension fund optimizes its retribution which is a part of the surplus. Then we define the optimal guarantee as the solution of the contributor's optimization program and find the solution explicitly. Finally, we analyze the impact of the main parameters, and particularly the sharing sule between the contributor and the pension fund. We find that favorable sharing rules for the pension fund lead to conservative guarantees for the contributor: the sharing rule is a way to create a continuum between the extreme points that are Defined Benefit and Defined Contribution Pension Schemes, and allows partial risk transfer between the contributor and the pension fund manager.