In this paper we consider a general optimal consumption and portfolio selection problem of a finitely-lived agent whose consumption rate process is subject to time-varying subsistence consumption constraints. That is, her consumption rate should be greater than or equal to some convex, non-decreasing and continuous function of time t. Using martingale duality approach and Feynman–Kac formula, we derive the partial differential equation of the Cauchy problem satisfied by the dual value function. We use the integral transform method for solving this Cauchy problem to obtain the general optimal policies in an explicit form. With constant relative risk aversion and constant absolute risk aversion utility functions we illustrate some numerical results of the optimal policies.

中文翻译：

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具有时变生存消费约束的有限时域最优投资和消费

在本文中，我们考虑了有限寿命代理的一般最优消费和投资组合选择问题，其消费率过程受时变生存消费约束。也就是说，她的消费率应该大于或等于时间 t 的某个凸的、非递减的连续函数。使用鞅对偶方法和Feynman-Kac公式，我们导出了满足对偶值函数的柯西问题的偏微分方程。我们使用积分变换方法来解决这个柯西问题，以获得显式形式的一般最优策略。使用恒定的相对风险厌恶和恒定的绝对风险厌恶效用函数，我们说明了最优策略的一些数值结果。