Optimization of Wealth Investment Strategies for a DC Pension Fund with Stochastic Salary and Extra Contributions

We studied optimal investment strategies for a plan contributor in a defined pension scheme, with stochastic salary and extra contributions, under the affine interest rate model. We considered two cases; where the extra contribution rates are stochastic and constant. We considered investment in three different assets namely risk free asset (cash), zero coupon bonds and the risky asset (stock). Using Legendre transformation method and dual theory, we obtained the optimal investment strategies the three investments using exponential utility function for the two cases. The result shows that the strategies for the respective investments used when there is no extra contribution can be used when the extra contribution rate is constant as in [1] but cannot be used when it is stochastic. Clearly this gives the member and the fund manager good insight on how to invest to maximize profit with minimal risk once this condition arises.