Consistent price systems and face-lifting pricing under transaction costs

• 成果类型: Article
• 署名作者: Guasoni, Paolo; Rasonyi, Mikloz; Schachermayer, Walter
• 署名单位: Boston University; HUN-REN; HUN-REN Institute for Computer Science & Control; Hungarian Academy of Sciences; Technische Universitat Wien
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/07-AAP461
• 发表日期: 2008
• 页码: 491-520
• 关键词: fractional brownian-motion; super-replication problem; finite discrete-time; fundamental theorem; no-arbitrage; MARKETS; version; MODEL

摘要

In markets with transaction costs, consistent price systems play the same role as martingale measures in frictionless markets. We prove that if a continuous price process has conditional full support, then it admits consistent price systems for arbitrarily small transaction costs. This result applies to a large class of Markovian and non-Markovian models, including geometric fractional Brownian motion. Using the constructed price systems, we show, under very general assumptions, the following face-lifting result: the asymptotic superreplication price of a European contingent claim g(S-T) equals (g) over cap (S-0), where (g) over cap is the concave envelope of g and S-t is the price of the asset at time t. This theorem generalizes similar results obtained for diffusion processes to processes with conditional full support.