摘要翻译：
我们将资产定价的基本定理推广到一个模型，其中风险股票服从以买卖价差形式出现的比例交易费用，银行账户具有不同的借贷利率。我们证明了这样一个模型是无套利的当且仅当人们可以在它中嵌入一个无摩擦模型，该模型本身是无套利的，在这个意义上，股票的出出价和出出价之间存在一个人为的无摩擦价格，借贷利率之间存在一个人为的利率，这样，如果人们用这个利率折价这个股票价格，那么所得到的过程是一个在某种非退化概率测度下的鞅。将我们自己限制在股票价格的有限个时间步骤和有限个可能结果的简单情况下，通过结合基于有限维分离定理的经典论点和线性优化的对偶结果来证明。
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英文标题：
《The fundamental theorem of asset pricing under proportional transaction
  costs》
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作者：
Alet Roux
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最新提交年份：
2007
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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 extend the fundamental theorem of asset pricing to a model where the risky stock is subject to proportional transaction costs in the form of bid-ask spreads and the bank account has different interest rates for borrowing and lending. We show that such a model is free of arbitrage if and only if one can embed in it a friction-free model that is itself free of arbitrage, in the sense that there exists an artificial friction-free price for the stock between its bid and ask prices and an artificial interest rate between the borrowing and lending interest rates such that, if one discounts this stock price by this interest rate, then the resulting process is a martingale under some non-degenerate probability measure. Restricting ourselves to the simple case of a finite number of time steps and a finite number of possible outcomes for the stock price, the proof follows by combining classical arguments based on finite-dimensional separation theorems with duality results from linear optimisation.
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PDF链接：
https://arxiv.org/pdf/0710.2758