Non-addictive habits: optimal consumption-portfolio policies

• 成果类型: Article
• 署名作者: Detemple, JB; Karatzas, I
• 署名单位: Boston University; Columbia University; Columbia University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/S0022-0531(03)00099-1
• 发表日期: 2003
• 页码: 265-285
• 关键词: habit formation; non-addiction; constrained consumption-portfolio optimization; stopping times; recursive (backward) stochastic equations and inequalities; Asian capped options

摘要

We formulate a model of preferences with non-addictive habits, where consumption is required to be non-negative at all times, but can fall below a standard of living index that aggregates past consumption. We study the consumption-portfolio problem taking account of the non-negativity constraint on consumption, and provide a constructive proof for the existence of an optimal policy on a finite time-horizon [0, T]. We show that the consumption constraint binds up to an endogenous stopping time tau* epsilon [0, T], after which it remains slack until T. A decomposition of constrained consumption involving an Asian average-strike capped call-option is demonstrated. (C) 2003 Elsevier Inc. All rights reserved.