The existence, uniqueness, and optimality of the terminal wealth depletion time in life-cycle models of saving under uncertain lifetime and borrowing constraint

• 成果类型: Article; Proceedings Paper
• 署名作者: Leung, Sin Fai
• 署名单位: Hong Kong University of Science & Technology
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2006.05.004
• 发表日期: 2007
• 页码: 470-493
• 关键词: life-cycle saving; uncertain lifetime; Borrowing constraint; wealth depletion; state-constrained maximum principle

摘要

In life-cycle models of saving under uncertain lifetime and borrowing constraint, the consumer's wealth must be depleted before the maximum lifetime. This paper investigates the existence, uniqueness, and optimality of the terminal wealth depletion time. It is proved that the optimal terminal wealth depletion time, if such exists, must be unique. If the equation that determines the optimal terminal wealth depletion has multiple solutions, then the location of the optimal solution will depend on the configuration of the solutions. An optimality test is developed to verify whether a candidate solution for the terminal wealth depletion time is indeed optimal. The paper introduces a method new to economics, the Dubovitskii-Milyutin adjoint equation, to analyze the properties of the optimal control problem. (c) 2006 Elsevier Inc. All rights reserved.