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 have a minimum guarantee for the final annuity, a safety level for the wealth process is considered. To solve the stochastic optimal control problem via dynamic programming, we obtain a Hamilton-Jacobi-Bellman (HJB) equation on a bounded domain. The existence and uniqueness of classical solutions are proved through the dual transformation. We apply the finite difference method to find numerical approximations of the solution of the HJB equation. Finally, the simulation results for the optimal investment-consumption strategies, optimal wealth process and the final annuity for different admissible ranges of consumption are given . Furthermore, by taking into account the market present value of the cash flows before and after the annuitization, we compare the outcomes of different scenarios .
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eliminate the ruin possibilities and having
have
D
we consider
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which consequently yields
is considered. To solve the stochastic optimal control problem via dynamic programming, we obtain
A
The existence and uniqueness of classical solutions are proved through the dual transformation.
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policy iteration
finite difference
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approximations of
numerical approximations of the
D
we give
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ranges of admissible consumptions
admissible ranges of consumption are given
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calculating the present market
taking into account the market present
D
future
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results for different consumption policies
outcomes of different scenarios