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

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

We study the optimal investment-consumption problem for a member of defined contribution plan during the decumulation phase. For a fixed annuitization time, to achieve higher final annuity, we consider a variable consumption rate. Moreover, to eliminate the ruin possibilities and having a minimum guarantee for the final annuity, we consider a safety level for the wealth process which consequently yields a Hamilton-Jacobi-Bellman (HJB) equation on a bounded domain. We apply the policy iteration method to find approximations of solution of the HJB equation. Finally, we give the simulation results for the optimal investment-consumption strategies, optimal wealth process and the final annuity for different ranges of admissible consumptions. Furthermore, by calculating the present market value of the future cash flows before and after the annuitization, we compare the results for different consumption policies.

We study the optimal investment-consumption problem for a member of defined contribution plan during the decumulation phase. For a fixed annuitization time, to achieve higher final annuity, we consider a variable consumption rate. Moreover, to eliminate the ruin possibilities and having a minimum guarantee for the final annuity, we consider a safety level for the wealth process which consequently yields a Hamilton-Jacobi-Bellman (HJB) equation on a bounded domain. We apply the policy iteration method to find approximations of solution of the HJB equation. Finally, we give the simulation results for the optimal investment-consumption strategies, optimal wealth process and the final annuity for different ranges of admissible consumptions. Furthermore, by calculating the present market value of the future cash flows before and after the annuitization, we compare the results for different consumption policies.