This paper studies the optimal consumption-investment-annuitization problem for a retiree with linear consumption habits. We explore the effect of consumption habits on the decision to annuitize when annuities are purchased as a lump sum. The problem is formulated as a combined stopping-control problem. We derive optimal annuitization time, investment, and consumption strategies by a generalized dual method and habit reduction method. We investigate the influence of various factors on the annuitization time and derive optimal annuitization time, which is a barrier strategy. The numerical simulations reveal several interesting results. Our results demonstrate that risk aversion, subjective hazard rate, and consumption habits all play a role in shaping annuitization decisions. Furthermore, we offer a new explanation for the rarity of voluntary annuitization among retirees.

本文研究具有线性消费习惯的退休人员的最优消费-投资-年金问题。我们探讨一次性购买年金时消费习惯对年金决定的影响。该问题被表述为组合的停止控制问题。我们通过广义对偶方法和习惯减少方法得出最佳年金化时间、投资和消费策略。我们研究了各种因素对年金化时间的影响，并得出最佳年金化时间，这是一种障碍策略。数值模拟揭示了一些有趣的结果。我们的结果表明，风险厌恶、主观风险率和消费习惯都在影响年金决策中发挥着作用。此外，我们对退休人员自愿年金很少见的情况提供了新的解释。