SHADOW PRICE IN THE POWER UTILITY CASE

• 成果类型: Article
• 署名作者: Herczegh, Attila; Prokaj, Vilmos
• 署名单位: Eotvos Lorand University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1058
• 发表日期: 2015
• 页码: 2671-2707
• 关键词: transaction costs; PORTFOLIO SELECTION; Optimal investment; consumption; MODEL

摘要

We consider the problem of maximizing expected power utility from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in Shreve and Soner [Ann. Appl. Probab. 4 (1994) 609-692]. Similar to Kallsen and Muhle-Karbe [Ann. Appl. Probab. 20 (2010) 1341-1358], we derive a shadow price, that is, a frictionless price process with values in the bid-ask spread which leads to the same optimal policy.