DUALITY THEORY FOR PORTFOLIO OPTIMISATION UNDER TRANSACTION COSTS

• 成果类型: Article
• 署名作者: Czichowsky, Christoph; Schachermayer, Walter
• 署名单位: University of London; London School Economics & Political Science; University of Vienna
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1136
• 发表日期: 2016
• 页码: 1888-1941
• 关键词: trading strategies; Optimal investment; MARKET; selection; arbitrage

摘要

We consider the problem of portfolio optimisation with general cadlag price processes in the presence of proportional transaction costs. In this context, we develop a general duality theory. In particular, we prove the existence of a dual optimiser as well as a shadow price process in an appropriate generalised sense. This shadow price is defined by means of a sandwiched process consisting of a predictable and an optional strong supermartingale, and pertains to all strategies that remain solvent under transaction costs. We provide examples showing that, in the general setting we study, the shadow price processes have to be of such a generalised form.