DC Pension Plan with Refund of Contributions under Affine Interest Rate Model

Main Article Content

Udeme O. Ini
Obinichi C. Mandah
Edikan E. Akpanibah


This paper studies the optimal investment plan for a pension scheme with refund of contributions, stochastic salary and affine interest rate model. A modified model which allows for refund of contributions to death members’ families is considered. In this model, the fund managers invest in a risk free (treasury) and two risky assets (stock and zero coupon bond) such that the price of the risky assets are modelled by geometric Brownian motions and the risk free interest rate is of affine structure. Using the game theoretic approach, an extended Hamilton Jacobi Bellman (HJB) equation which is a system of non linear PDE is established. Furthermore, the extended HJB equation is then solved by change of variable and variable separation technique to obtain explicit solutions of the optimal investment plan for the three assets using mean variance utility function. Finally, theoretical analyses of the impact of some sensitive parameters on the optimal investment plan are presented.

Pension scheme, extended HJB equation, investment plan, refund clause, stochastic salary, affine interest rate.

Article Details

How to Cite
Ini, U. O., Mandah, O. C., & Akpanibah, E. E. (2020). DC Pension Plan with Refund of Contributions under Affine Interest Rate Model. Asian Journal of Probability and Statistics, 7(2), 1-16. https://doi.org/10.9734/ajpas/2020/v7i230175
Original Research Article


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