Change of numeraire in the two-marginals martingale transport problem
Change of numeraire in the two-marginals martingale transport problem
复制标题
二边鞅运输问题中计价单位的变化
DOI：
10.1007/s00780-016-0322-2
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发表时间：
2014
影响因子：
1.7
通讯作者：
C. Martini
中科院分区：
文献类型：
--
作者：
L. Campi;Ismail Laachir;C. Martini
本文将数值变换技术应用于计算两期条件下衍生产品无模型价格的最优传输方法。特别是，我们考虑了在霍布森和Klimmek(Finance Stoch)建立的最优运输计划。19：189-214,2015)以及在Beiglböck和Juillet(Ann)中介绍的那个。可能吧。44：42-106,2016)，并在Henry-Labdère和Touzi(Finance Stoch)深造。2016年20：635-668)。我们证明了，在正鞅的情况下，一个适当的数字变化适用于Hobson和Klimmek(Finance Stoch)。19：189-214,2015)交易所远期开始跨越I型和II型，因此子套期保值问题中的最优运输计划对于这两种类型的期权是相同的。此外，对于亨利-拉博代尔和图兹(Finance Stoch.2016：635-668)建设，右单调调运方案可以看作是数字变化下左调调方案的镜像耦合。
In this paper, we apply change of numeraire techniques to the optimal transport approach for computing model-free prices of derivatives in a two-period setting. In particular, we consider the optimal transport plan constructed in Hobson and Klimmek (Finance Stoch. 19:189–214, 2015) as well as the one introduced in Beiglböck and Juillet (Ann. Probab. 44:42–106, 2016) and further studied in Henry-Labordère and Touzi (Finance Stoch. 20:635–668, 2016). We show that in the case of positive martingales, a suitable change of numeraire applied to Hobson and Klimmek (Finance Stoch. 19:189–214, 2015) 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 Henry-Labordère and Touzi’s (Finance Stoch. 20:635–668, 2016) construction, the right-monotone transference plan can be viewed as a mirror coupling of its left counterpart under the change of numeraire.