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摘要翻译：
这项工作旨在更深入地理解金融市场中没有第一类套利的经济合理条件的数学含义。本文根据资产定价基本定理(FTAP)的精神，证明了在市场上没有第一类套利就相当于存在一个有限可加概率，弱等价于原始的且仅局部可数可加，在此条件下，财富折现过程成为“局部鞅”。然后利用上述结果得到了Delbaen和Schachermayer的FTAP的独立证明。最后，本文对连续路径半鞅资产价格过程的情形作了简单而简短的讨论。
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英文标题：
《Finitely additive probabilities and the Fundamental Theorem of Asset
Pricing》
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作者：
Constantinos Kardaras
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最新提交年份：
2009
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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：Quantitative Finance 数量金融学
二级分类：General Finance 一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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英文摘要：
This work aims at a deeper understanding of the mathematical implications of the economically-sound condition of absence of arbitrages of the first kind in a financial market. In the spirit of the Fundamental Theorem of Asset Pricing (FTAP), it is shown here that absence of arbitrages of the first kind in the market is equivalent to the existence of a finitely additive probability, weakly equivalent to the original and only locally countably additive, under which the discounted wealth processes become "local martingales". The aforementioned result is then used to obtain an independent proof of the FTAP of Delbaen and Schachermayer. Finally, an elementary and short treatment of the previous discussion is presented for the case of continuous-path semimartingale asset-price processes.
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PDF链接：
https://arxiv.org/pdf/0911.5503
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