Canadian Journal of Pure & Applied Sciences

Abstract: This paper merged together the study of optimal control laws for a pension plan with and without return clause under Heston volatility model. An investment model comprising of members’ monthly contributions, return accumulations with risk free interest to dead members’ families for the case with return clause and investment in one risk free asset and two risky assets is presented. Since the mean variance utility function is time inconsistent, the game theoretic approach is used to establish an optimization problem from the extended Hamilton Jacobi Bellman (HJB) equation. Furthermore, the optimal control laws for the three assets and the efficient frontier are obtained using variable separation method by solving the extended HJB equations. Finally, Numerical simulations were presented to demonstrate the effects of some parameters on the optimal control laws with observations that the optimal control law for risk free asset decreases continuously with time while that of the risky assets increases continuously with time.