We compute the optimal dynamic annuitization and asset allocation policy for a retiree with Epstein–Zin preferences, uncertain investment horizon, potential bequest motives, and pre-existing pension income. In our setting the retiree can decide each year how much he consumes and how much he invests in stocks, bonds, and life annuities, while the prior literature mostly considered restricted so-called deterministic or stochastic switching strategies. We show that postponing the annuity purchase is no longer optimal in the gradual annuitization (GA) case since investors are able to attain the optimal mix between liquid assets (stocks and bonds) and illiquid life annuities each year. In order to assess potential utility losses, we benchmark various restricted annuitization strategies against the unrestricted GA strategy.