@article{Akpanibah_Ini_2021, title={Refund Clause of Contributions with Predetermined Interest under CEV Model}, volume={7}, url={http://ijmso.unilag.edu.ng/article/view/1207}, abstractNote={<p>This work studies the optimal control strategy for a pension plan with refund clause of contri-<br>butions with predetermined interest under constant elasticity of variance (CEV) in a defined<br>contribution (DC) pension plan. A model which mandates fund managers to refund dead mem-<br>bers’ accumulations with predetermined interest to their next of kin during the accumulation<br>phase is considered. Also considered herein are investments in a bank security and stock where<br>the stock market price is driven by the CEV model and the remaining accumulations are equally<br>distributed between the remaining members. Furthermore, the game theoretic approach is use<br>in establishing an optimization problem from the extended Hamilton Jacobi Bellman (HJB)<br>equation which is a non-linear partial differential equation (PDE). Using mean variance utility<br>function and method of variable separation, explicit solutions of the optimal control strategy<br>and the efficient frontier are obtained. Finally, Numerical simulations and theoretical analysis<br>are used to study the effect of the elasticity parameter β and some other parameters on the<br>optimal control strategy with observations that the elasticity parameter affects the investment<br>strategy of the fund manager significantly. Also, we observed that the optimal control strategy<br>employed by the fund manager is inversely proportional to the risk aversion coefficient, initial<br>fund size, instantaneous volatility and predetermined interest rate but directly proportional to<br>time.</p>}, number={1}, journal={International Journal of Mathematical Sciences and Optimization: Theory and Applications}, author={Akpanibah, C. E. and Ini, U. O.}, year={2021}, month={Mar.}, pages={1 - 16} }