Asian Journal of Probability and Statistics 7(2): 1-16, 2020; Article no.AJPAS.56313 ISSN: 2582-0230 _____________________________________ *Corresponding author: E-mail: edikanakpanibah@gmail.com; DC Pension Plan with Refund of Contributions under Affine Interest Rate Model Udeme O. Ini 1 , Obinichi C. Mandah 2 and Edikan E. Akpanibah 3* 1 Department of Mathematics and Computer Science, Niger Delta University, Bayelsa, Nigeria. 2 Department of Mathematics, University of Ibadan, Ibadan, Oyo State, Nigeria. 3 Department of Mathematics and Statistics, Federal University Otuoke, Bayelsa, Nigeria. Authors’ contributions This work was carried out by the three authors. Authors UOI and OCM developed and solved the model. Author EEA did the theoretical analyses and interpretations and authors UOI and OCM wrote the literature of the work. All the authors approved the final manuscript. Article Information DOI: 10.9734/AJPAS/2020/v7i230175 Editor(s): (1) Dr. S. M. Aqil Burney, University of Karachi, Pakistan. Reviewers: (1) Hugo Cruz-Suárez, Benemérita Universidad Autónoma de Puebla, Mexico. (2) Xiangrong Wang, Shandong University of Science and Technology, China. Complete Peer review History: http://www.sdiarticle4.com/review-history/56313 Received: 10 February 2020 Accepted: 18 April 2020 Published: 07 May 2020 _______________________________________________________________________________ Abstract 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. Keywords: Pension scheme; extended HJB equation; investment plan; refund clause; stochastic salary; affine interest rate. 2010 Mathematics Subject Classification: 91B16, 90C31, 62P05. Original Research Article