摘要翻译：
本文的目的有二。首先，将n维半鞅及其随机积分的概念推广到随机维数的分段半鞅。前者的性质在很大程度上完整地延续到后者，避免了无限维随机积分的一些陷阱。二是推广了资产定价的两个基本定理：无风险消失的免费午餐等价于价格过程存在等价的σ鞅测度；无第一类套利等价于非负财富过程集合存在等价的局部鞅平减指数。
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英文标题：
《Fundamental theorems of asset pricing for piecewise semimartingales of
  stochastic dimension》
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作者：
Winslow Strong
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最新提交年份：
2011
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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：
  The purpose of this paper is two-fold. First is to extend the notions of an n-dimensional semimartingale and its stochastic integral to a piecewise semimartingale of stochastic dimension. The properties of the former carry over largely intact to the latter, avoiding some of the pitfalls of infinite-dimensional stochastic integration. Second is to extend two fundamental theorems of asset pricing (FTAPs): the equivalence of no free lunch with vanishing risk to the existence of an equivalent sigma-martingale measure for the price process, and the equivalence of no arbitrage of the first kind to the existence of an equivalent local martingale deflator for the set of nonnegative wealth processes.
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PDF链接：
https://arxiv.org/pdf/1112.5340