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摘要翻译：
在一个具有固定债券和几种风险资产的贴现市场中，我们用简单的交易策略来刻画套利的缺失。我们证明了如果存在一个简单套利，那么存在一个0-允许的套利或一个明显的套利，即一个承诺最小无风险收益\ε的简单套利，如果投资者进行交易。对于连续股票模型，我们根据路径的精细结构性质，给出了不存在0-容许的简单套利的等价条件，我们称之为“双向交叉”。这种性质可以通过重对数定律对许多模型进行验证。作为一个应用，我们证明了Hurst参数大于一半的混合分数Black-Scholes模型在紧时间范围内是不存在简单套利的。更一般地说，我们讨论了随机波动率模型和局部波动率模型在一个独立的1/2-H\“{o}lder连续过程扰动下不存在简单套利的问题。
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英文标题：
《Simple arbitrage》
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作者：
Christian Bender
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最新提交年份：
2012
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
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 \epsilon, 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-H\"{o}lder continuous process.
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PDF链接：
https://arxiv.org/pdf/1210.5391
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