Fundamental Theorem of Asset Pricing Under Transaction Costs and Model Uncertainty

• 成果类型: Article
• 署名作者: Bayraktar, Erhan; Zhang, Yuchong
• 署名单位: University of Michigan System; University of Michigan; Columbia University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2015.0767
• 发表日期: 2016
• 页码: 1039-1054
• 关键词: arbitrage

摘要

We prove the fundamental theorem of asset pricing for a discrete time financial market where trading is subject to proportional transaction costs and the asset price dynamic is modeled by a family of probability measures, possibly nondominated. Using a backward-forward scheme, we show that when the market consists of a money market account and a single stock, no-arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of consistent price systems. We also show that when the market consists of multiple dynamically traded assets and satisfies efficient friction, strict no-arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of strictly consistent price systems.