标题： 在年龄依赖的死亡率强度下具有劳动收入的最优年金化 显示英文标题

标题： Optimal annuitization with labor income under age-dependent force of mortality

摘要： 我们考虑与劳动收入相结合的最优年金化问题，其中代理人旨在在年龄相关的死亡率强度下最大化消费和劳动收入的效用。 使用动态规划方法，我们推导出价值函数以及最优消费、投资和劳动供给策略的显式解。 我们的结果表明，在退休前，投资行为随着财富的增加而增加，直到由劳动供给设定的阈值。 退休后，代理人倾向于消费其财富的更大比例。 两个主要因素影响人们年龄增长时的最优年金化决策。 首先，代理人的视角（需求方）；代理人的个人贴现率随年龄增长而上升，降低了他们进行年金化的意愿。 其次，保险人的视角（供给方）；保险公司提供更高的赔付率（死亡率红利）。 我们的模型表明，超过一定年龄后，急剧下降的生存概率使年金化变得非常最优，因为死亡率红利的强大激励超过了代理人的高个人贴现率。 最后，退休后的劳动收入通过提供另一种稳定收入来源，直接替代了年金化。 它增强了退休人员的财务安全性。 显示英文摘要

摘要： We consider the problem of optimal annuitization with labour income, where an agent aims to maximize utility from consumption and labour income under age-dependent force of mortality. Using a dynamic programming approach, we derive closed-form solutions for the value function and the optimal consumption, portfolio, and labor supply strategies. Our results show that before retirement, investment behavior increases with wealth until a threshold set by labor supply. After retirement, agents tend to consume a larger portion of their wealth. Two main factors influence optimal annuitization decisions as people get older. First, the agent's perspective (demand side); the agent's personal discount rate rises with age, reducing their desire to annuitize. Second, the insurer's perspective (supply side); insurers offer higher payout rates (mortality credits). Our model demonstrates that beyond a certain age, sharply declining survival probabilities make annuitization substantially optimal, as the powerful incentive of mortality credits outweighs the agent's high personal discount rate. Finally, post-retirement labor income serves as a direct substitute for annuitization by providing an alternative stable income source. It enhances the financial security of retirees.