SIMPLE ARBITRAGE

• 成果类型: Article
• 署名作者: Bender, Christian
• 署名单位: Saarland University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/11-AAP830
• 发表日期: 2012
• 页码: 2067-2085
• 关键词: fractional brownian-motion; no-arbitrage; stochastic volatility; transaction costs; SEMIMARTINGALES; models

摘要

We characterize absence of arbitrage with simple trading strategies in a discounted market with a constant bond and several risky assets. We show that if there is a simple arbitrage, then there is a 0-admissible one or an obvious one, that is, a simple arbitrage which promises a minimal riskless gain of E, if the investor trades at all. For continuous stock models, we provide an equivalent condition for absence of 0-admissible simple arbitrage in terms of a property of the fine structure of the paths, which we call two-way crossing. This property can be verified for many models by the law of the iterated logarithm. As an application we show that the mixed fractional Black-Scholes model, with Hurst parameter bigger than a half, is free of simple arbitrage on a compact time horizon. More generally, we discuss the absence of simple arbitrage for stochastic volatility models and local volatility models which are perturbed by an independent 1/2-Holder continuous process.