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The essence of this research is to study the optimal investment strategy for a plan contributor in a defined contribution (DC) pension scheme, with stochastic salary and stochastic extra contribution, under the affine interest rate model. We considered the Nigerian Pension Reform Act of 2004 which allow members to contribute an additional proportion of their income into the pension account different from the mandatory contribution. Also we considered investment in cash, zero coupon bond and stock. By using Legendre transformation method and dual theory we obtained the optimal investment strategies for the three investments under the exponential utility function. We observed that the extra contribution has an effect on the optimal investment strategies. The result shows that the pension member will reduce the proportion of his wealth to be invested in cash and increase the proportion to be invested in bond and stock.

general letters in mathematics

On the Effect of Stochastic Extra Contribution on Optimal Investment Strategies for Stochastic Salary Under the Affine Interest Rate Model in a DC pension Fund