The purpose of this paper is to study the optimal retirement and consumption/investment decisions of an infinitely lived agent who does not tolerate any decline in his/her consumption throughout his/her lifetime. The agent receives labor income but suffers disutility from working until retirement. The agent’s optimization problem combines features of both singular control and optimal stopping. We use the martingale method and study the dual problem, which can be decoupled into a singular control problem and an optimal stopping problem. We provide a closed-form solution of the optimal strategies for the von Neumann–Morgenstern utility function. We show that the coefficient of relative risk aversion implied by the optimal portfolio (i.e., the implied coefficient of relative risk aversion, ICRRA) is a constant value smaller than 1. Moreover, we show that the ICRRA is independent of the agent’s felicity utility function and depends only on the subjective discount rate and market parameters.

中文翻译：

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消耗增加，优化退休和投资组合选择

本文的目的是研究无限生存的代理商的最优退休和消费/投资决策，该代理商在其一生中均不容许其消费量的任何下降。代理人获得劳动收入，但从工作到退休都无济于事。代理的优化问题结合了奇异控制和最佳停止的特点。我们使用the方法研究了对偶问题，它可以解耦为奇异控制问题和最优停车问题。我们为冯·诺依曼–摩根斯滕效用函数的最优策略提供了一种封闭形式的解决方案。我们表明，最优投资组合所隐含的相对风险规避系数（即隐性相对风险规避系数ICRRA）是一个小于1的常数。