英文标题：
《Portfolio optimisation beyond semimartingales: shadow prices and
fractional Brownian motion》
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作者：
Christoph Czichowsky and Walter Schachermayer
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最新提交年份：
2016
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英文摘要：
While absence of arbitrage in frictionless financial markets requires price processes to be semimartingales, non-semimartingales can be used to model prices in an arbitrage-free way, if proportional transaction costs are taken into account. In this paper, we show, for a class of price processes which are not necessarily semimartingales, the existence of an optimal trading strategy for utility maximisation under transaction costs by establishing the existence of a so-called shadow price. This is a semimartingale price process, taking values in the bid ask spread, such that frictionless trading for that price process leads to the same optimal strategy and utility as the original problem under transaction costs. Our results combine arguments from convex duality with the stickiness condition introduced by P. Guasoni. They apply in particular to exponential utility and geometric fractional Brownian motion. In this case, the shadow price is an Ito process. As a consequence we obtain a rather surprising result on the pathwise behaviour of fractional Brownian motion: the trajectories may touch an Ito process in a one-sided manner without reflection.
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中文摘要：
虽然在无摩擦金融市场中没有套利要求价格过程是半鞅，但如果考虑到比例交易成本，非半鞅可以用于以无套利的方式建模价格。本文通过建立影子价格的存在性，证明了一类不一定是半鞅的价格过程在交易成本下效用最大化的最优交易策略的存在性。这是一个半鞅价格过程，考虑买卖价差中的价值，这样，在交易成本下，该价格过程的无摩擦交易会产生与原始问题相同的最优策略和效用。我们的结果结合了凸对偶的论点和P.Guasoni引入的粘性条件。它们特别适用于指数效用和几何分数布朗运动。在这种情况下，影子价格是一个Ito过程。因此，对于分数布朗运动的路径行为，我们得到了一个相当令人惊讶的结果：轨迹可能会以单边方式接触Ito过程，而没有反射。
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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：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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