英文标题：
《Change of numeraire in the two-marginals martingale transport problem》
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作者：
Luciano Campi, Ismail Laachir, Claude Martini
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最新提交年份：
2016
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英文摘要：
In this paper we apply change of numeraire techniques to the optimal transport approach for computing model-free prices of derivatives in a two periods model. In particular, we consider the optimal transport plan constructed in \\cite{HobsonKlimmek2013} as well as the one introduced in \\cite{BeiglJuil} and further studied in \\cite{BrenierMartingale}. We show that, in the case of positive martingales, a suitable change of numeraire applied to \\cite{HobsonKlimmek2013} exchanges forward start straddles of type I and type II, so that the optimal transport plan in the subhedging problems is the same for both types of options. Moreover, for \\cite{BrenierMartingale}\'s construction, the right monotone transference plan can be viewed as a mirror coupling of its left counterpart under the change of numeraire. An application to stochastic volatility models is also provided.
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中文摘要：
在本文中，我们将数值变化技术应用于最优运输方法，以计算两阶段模型中衍生品的无模型价格。特别地，我们考虑了在{HobsonKlimmek2013}中构造的最优运输计划，以及在{BeiglJuil}中引入并在{Brenier鞅}中进一步研究的最优运输计划。我们证明，在正鞅的情况下，适用于类型I和类型II的{HobsonKlimmek2013}交换前向启动跨座的适当数值变化，因此，对于两种类型的选项，分边问题中的最优运输计划是相同的。此外，对于{Brenier鞅}的结构，右单调转移计划可以被视为其左对应物在数值变化下的镜像耦合。还提供了随机波动率模型的应用。
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分类信息：

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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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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