Utility maximization with a stochastic clock and an unbounded random endowment

• 成果类型: Article
• 署名作者: Zitkovic, G
• 署名单位: Carnegie Mellon University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000738
• 发表日期: 2005
• 页码: 748-777
• 关键词: Incomplete markets; fundamental theorem; Optimal investment; OPTIMAL PORTFOLIO; bipolar theorem; consumption; version

摘要

We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and uniqueness for a large class of utility-maximization problems including the classical ones of terminal wealth or consumption, as well as the problems that depend on a random time horizon or multiple consumption instances. As an example we explicitly treat the problem of maximizing the logarithmic utility of a consumption stream, where the local time of an Ornstein-Uhlenbeck process acts as a stochastic clock.