TY - JOUR
AU - C. E. Akpanibah
AU - U. O. Ini
PY - 2021/03/29
Y2 - 2021/04/23
TI - Refund Clause of Contributions with Predetermined Interest under CEV Model
JF - International Journal of Mathematical Sciences and Optimization: Theory and Applications
JA - IJMSO
VL - 7
IS - 1
SE - Articles
DO -
UR - http://ijmso.unilag.edu.ng/article/view/1207
AB - This work studies the optimal control strategy for a pension plan with refund clause of contri-butions with predetermined interest under constant elasticity of variance (CEV) in a definedcontribution (DC) pension plan. A model which mandates fund managers to refund dead mem-bers’ accumulations with predetermined interest to their next of kin during the accumulationphase is considered. Also considered herein are investments in a bank security and stock wherethe stock market price is driven by the CEV model and the remaining accumulations are equallydistributed between the remaining members. Furthermore, the game theoretic approach is usein establishing an optimization problem from the extended Hamilton Jacobi Bellman (HJB)equation which is a non-linear partial differential equation (PDE). Using mean variance utilityfunction and method of variable separation, explicit solutions of the optimal control strategyand the efficient frontier are obtained. Finally, Numerical simulations and theoretical analysisare used to study the effect of the elasticity parameter β and some other parameters on theoptimal control strategy with observations that the elasticity parameter affects the investmentstrategy of the fund manager significantly. Also, we observed that the optimal control strategyemployed by the fund manager is inversely proportional to the risk aversion coefficient, initialfund size, instantaneous volatility and predetermined interest rate but directly proportional totime.
ER -