Optimal investment-consumption problem post-retirement with a minimum guarantee

We study the optimal investment-consumption problem for a member of de ned contribution plan during the decumulation phase. For a xed annuitization time, to achieve higher nal annuity, we consider a variable consumption rate. Moreover, to have a minimum guarantee for the nal annuity, a safety level for the wealth process is considered. To solve the stochastic optimal control problem via dynamic programing, we get a Hamilton-Jacobi-Bellman (HJB) equation on a bounded domain. We apply the policy iteration method to nd approximations of solution of the HJB equation. Finally, the simulation results for the optimal investment-consumption strategies, optimal wealth process and the nal annuity for di erent admissible ranges of consumption are given. Furthermore, by taking into account the market present value of the cash ows before and after