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

TL;DR

This paper addresses the complex problem of optimizing investment and consumption strategies during the decumulation phase of retirement, incorporating guarantees and variable consumption to maximize final annuity.

Contribution

It introduces a novel stochastic control framework with a bounded domain HJB equation, proving existence and uniqueness of solutions, and provides numerical methods for practical implementation.

Findings

Optimal strategies depend on wealth and consumption constraints.

Guarantees improve final annuity outcomes under certain conditions.

Numerical simulations illustrate the impact of consumption ranges on retirement wealth.

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 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.