Pointwise Arbitrage Pricing Theory in Discrete Time

• 成果类型: Article
• 署名作者: Burzoni, Matteo; Frittelii, Marco; Hou, Zhaoxu; Maggis, Marco; Obloj, Jan
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Milan; University of Oxford
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2018.0956
• 发表日期: 2019
• 页码: 1034-1057
• 关键词: martingale optimal transport; fundamental theorem; Duality; maximum; options

摘要

We develop a robust framework for pricing and hedging of derivative securities in discrete-time financial markets. We consider markets with both dynamically and statically traded assets and make minimal measurability assumptions. We obtain abstract (pointwise) fundamental theorem of asset pricing and pricing-hedging duality. Our results are general and, in particular, cover both the so-called model independent case as well as the classical probabilistic case of Dalang-Morton-Willinger. Our analysis is scenario-based: a model specification is equivalent to a choice of scenarios to be considered. The choice can vary between all scenarios and the set of scenarios charged by a given probability measure. in this way, our framework interpolates between a model with universally acceptable broad assumptions and a model based on a specific probabilistic view of future asset dynamics.