Title: Optimal investment-consumption problem post-retirement with a minimum guarantee,
Abstract: 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.