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On a multi-asset version of the Kusuoka limit theorem of option superreplication under transaction costs
Finance and Stochastics ( IF 1.7 ) Pub Date : 2020-12-30 , DOI: 10.1007/s00780-020-00441-4
Julien Grépat , Yuri Kabanov

We consider, using the geometric description, a sequence of models of multi-asset financial markets with proportional transaction costs vanishing in the limit. We assume that the price processes are He-type multinomial approximations of a process whose components are correlated geometric Brownian motions. For a given vector-valued contingent claim, defined as a continuous function of the price trajectories, we consider for each model the hedging set, that is, the set of all vector-valued initial endowments permitting to superreplicate the contingent claim by the final position of a self-financing portfolio. We calculate the limit of the hedging sets in the closed topology, obtaining in this way a set-valued version of the Kusuoka limit theorem.



中文翻译:

在多资产版本的Kusuoka交易成本下期权超复制的极限定理

我们考虑使用几何描述,建立一系列多资产金融市场模型,其中比例交易成本在极限内消失。我们假设价格过程是过程的He型多项式逼近,其组成部分是相关的几何布朗运动。对于定义为价格轨迹的连续函数的给定向量值或有债权,我们为每个模型考虑套期保值集合,即所有向量值初始initial赋的集合,这些集合可以通过最终仓位来复制或有债权自筹资金组合。我们计算封闭拓扑中对冲集的极限,以这种方式获得Kusuoka极限定理的集值版本。

更新日期:2020-12-30
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