ON UTILITY MAXIMIZATION UNDER CONVEX PORTFOLIO CONSTRAINTS

• 成果类型: Article
• 署名作者: Larsen, Kasper; Zitkovic, Gordan
• 署名单位: Carnegie Mellon University; University of Texas System; University of Texas Austin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/12-AAP850
• 发表日期: 2013
• 页码: 665-692
• 关键词: optimal investment; fundamental theorem; optimal consumption; optimization; prices

摘要

We consider a utility-maximization problem in a general semimartingale financial model, subject to constraints on the number of shares held in each risky asset. These constraints are modeled by predictable convex-set-valued processes whose values do not necessarily contain the origin; that is, it may be inadmissible for an investor to hold no risky investment at all. Such a setup subsumes the classical constrained utility-maximization problem, as well as the problem where illiquid assets or a random endowment are present. Our main result establishes the existence of optimal trading strategies in such models under no smoothness requirements on the utility function. The result also shows that, up to attainment, the dual optimization problem can be posed over a set of countably-additive probability measures, thus eschewing the need for the usual finitely-additive enlargement.