论文标题
劳动收入的退休后的最佳年金化
Optimal annuitization post-retirement with labor income
论文作者
论文摘要
有证据表明,退休年龄人群的劳动参与率不可忽略,这是全球广泛的现象。在美国,据劳工统计局报道,到2026年,75岁及以上工人的劳动力参与率预计将超过10%。退休后工作的普遍性改变了现有的最佳年鉴考虑因素,这一研究问题进一步归功于新的因素,例如退休后劳动率,工资率,能力或工作意愿。据我们所知,这构成了一个实用和理论问题,以前在精算文献中没有研究过。在本文中,我们研究了退休后年金化的问题,并在随机控制,最佳停止和预期的效用最大化的框架内额外的劳动收入和额外的劳动收入。实用程序功能是Cobb-Douglas类型的。 Martingale方法论和二元技术用于获得双重和原始问题的封闭式解决方案。通过利用明确的解决方案和蒙特卡洛模拟来研究劳动收入的影响。后者表明,在有或没有劳动收入的情况下,最佳的年金化时间与初始财富有关。当涉及到最佳的年鉴时,我们发现工资和劳动率可能起着相反的作用。但是,它们的影响是由杠杆比率介导的。
Evidence shows that the labor participation rate of retirement age cohorts is non-negligible, and it is a widespread phenomenon globally. In the United States, the labor force participation rate for workers age 75 and older is projected to be over 10 percent by 2026 as reported by the Bureau of Labor Statistics. The prevalence of post-retirement work changes existing considerations of optimal annuitization, a research question further complicated by novel factors such as post-retirement labor rates, wage rates, and capacity or willingness to work. To our knowledge, this poses a practical and theoretical problem not previously investigated in actuarial literature. In this paper, we study the problem of post-retirement annuitization with extra labor income in the framework of stochastic control, optimal stopping, and expected utility maximization. The utility functions are of the Cobb-Douglas type. The martingale methodology and duality techniques are employed to obtain closed-form solutions for the dual and primal problems. The effect of labor income is investigated by exploiting the explicit solutions and Monte-Carlo simulation. The latter reveals that the optimal annuitization time is strongly linear with respect to the initial wealth, with or without labor income. When it comes to optimal annuitization, we find that the wage and labor rates may play opposite roles. However, their impact is mediated by the leverage ratio.