Abstract
We study the optimal decumulation of retirement wealth under longevity and market risk. In particular, we focus on the transition between drawdown, which preserves liquidity and bequest potential, and annuitization, which provides a guaranteed lifetime income. We develop a flex-tofix framework in which retirees remain invested and liquid before converting part or all of their wealth into an annuity at a later date. The flex-to-fix strategy has two limiting cases: immediate annuitization (fix-now) and permanent drawdown (fix-never). A static actuarial analysis shows that the optimal fixed conversion date depends strongly on the bequest motive, the withdrawal rate, and the return of the drawdown portfolio. There is no single optimal annuitization age across retirees, although optimal dates tend to concentrate around age 65 (retirement) or ages 75–80. Then, we develop two dynamic formulations that allow the conversion decision to respond to the retiree’s realized wealth-income state. An optimalstopping formulation shows that a well-chosen fixed date already captures most of the value of delaying annuitization, while state-contingent timing adds only a small further gain. A Hamilton-Jacobi-Bellman variational inequality (HJBVI) formulation characterizes the free boundary governing a gradual transition from drawdown to annuity income. It also reveals an implicit bond effect of annuities on optimal equity allocation, and shows that spreading purchases over time substantially reduces market timing and ruin risk compared to single-date conversion rules. Finally, we propose approximating the HJBVI strategy with a simpler rule that spreads annuity purchases evenly across the flex window, once the optimal target date has been calibrated.
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