ARBITRAGE AND DUALITY IN NONDOMINATED DISCRETE-TIME MODELS

• 成果类型: Article
• 署名作者: Bouchard, Bruno; Nutz, Marcel
• 署名单位: Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris; Columbia University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1011
• 发表日期: 2015
• 页码: 823-859
• 关键词: CONTINGENT CLAIMS; fundamental theorem; prices

摘要

We consider a nondominated model of a discrete-time financial market where stocks are traded dynamically, and options are available for static hedging. In a general measure-theoretic setting, we show that absence of arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of martingale measures. In the arbitrage-free case, we show that optimal superhedging strategies exist for general contingent claims, and that the minimal superhedging price is given by the supremum over the martingale measures. Moreover, we obtain a nondominated version of the Optional Decomposition Theorem.