ON USING SHADOW PRICES IN PORTFOLIO OPTIMIZATION WITH TRANSACTION COSTS

• 成果类型: Article
• 署名作者: Kallsen, J.; Muhle-Karbe, J.
• 署名单位: University of Kiel; University of Vienna
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP648
• 发表日期: 2010
• 页码: 1341-1358
• 关键词: selection

摘要

In frictionless markets, utility maximization problems are typically solved either by stochastic control or by martingale methods. Beginning with the seminal paper of Davis and Norman [Math. Oper. Res. 15 (1990) 676-713], stochastic control theory has also been used to solve various problems of this type in the presence of proportional transaction costs. Martingale methods, on the other hand, have so far only been used to derive general structural results. These apply the duality theory for frictionless markets typically to a fictitious shadow price process lying within the bid-ask bounds of the real price process. In this paper, we show that this dual approach can actually be used for both deriving a candidate solution and verification in Merton's problem with logarithmic utility and proportional transaction costs. In particular, we determine the shadow price process.