英文标题：
《Arbitrage, hedging and utility maximization using semi-static trading
strategies with American options》
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作者：
Erhan Bayraktar and Zhou Zhou
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最新提交年份：
2016
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英文摘要：
We consider a financial market where stocks are available for dynamic trading, and European and American options are available for static trading (semi-static trading strategies). We assume that the American options are infinitely divisible, and can only be bought but not sold. In the first part of the paper, we work within the framework without model ambiguity. We first get the fundamental theorem of asset pricing (FTAP). Using the FTAP, we get the dualities for the hedging prices of European and American options. Based on the hedging dualities, we also get the duality for the utility maximization. In the second part of the paper, we consider the market which admits non-dominated model uncertainty. We first establish the hedging result, and then using the hedging duality we further get the FTAP. Due to the technical difficulty stemming from the non-dominancy of the probability measure set, we use a discretization technique and apply the minimax theorem.
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中文摘要：
我们考虑一个金融市场，股票可用于动态交易，欧洲和美国期权可用于静态交易（半静态交易策略）。我们假设美式期权是无限可分的，只能买不能卖。在本文的第一部分，我们在没有模型歧义的框架内工作。我们首先得到了资产定价的基本定理（FTAP）。利用FTAP，我们得到了欧洲和美国期权套期保值价格的二重性。基于套期保值的对偶性，我们也得到了效用最大化的对偶性。在本文的第二部分，我们考虑了允许非支配模型不确定性的市常我们首先建立套期保值结果，然后利用套期保值对偶进一步得到FTAP。由于概率测度集的非支配性导致了技术上的困难，我们使用了离散化技术并应用了极大极小定理。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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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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