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摘要翻译：
考虑一个美式期权，当在时间t行使时支付G(x^*_t)，其中G是一个正增函数，x^*_t:=\sup_{s\le t}X_s，X_s是在时间s时基础证券的价格。假设利率为零，我们证明，如果该期权的卖方以初始资本X_0\int_{X_0}^{\infty}G(x)x^{-2}dx（这是允许他对冲其头寸的最小初始资本）开始交易，则该期权的卖方可以通过交易标的证券来对冲其头寸。这导致了交易策略总是具有竞争力，既与给定策略的当前表现相竞争，也与迄今为止的最佳表现相竞争。它还导致了统计测试方法，避免牺牲太多的最大统计意义，他们在积累数据的过程中达到。
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英文标题：
《Probability-free pricing of adjusted American lookbacks》
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作者：
A. Philip Dawid, Steven de Rooij, Peter Grunwald, Wouter M. Koolen,
Glenn Shafer, Alexander Shen, Nikolai Vereshchagin, and Vladimir Vovk
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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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英文摘要：
Consider an American option that pays G(X^*_t) when exercised at time t, where G is a positive increasing function, X^*_t := \sup_{s\le t}X_s, and X_s is the price of the underlying security at time s. Assuming zero interest rates, we show that the seller of this option can hedge his position by trading in the underlying security if he begins with initial capital X_0\int_{X_0}^{\infty}G(x)x^{-2}dx (and this is the smallest initial capital that allows him to hedge his position). This leads to strategies for trading that are always competitive both with a given strategy's current performance and, to a somewhat lesser degree, with its best performance so far. It also leads to methods of statistical testing that avoid sacrificing too much of the maximum statistical significance that they achieve in the course of accumulating data.
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PDF链接：
https://arxiv.org/pdf/1108.4113
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