标题： 无套利与对冲液性美式期权 显示英文标题

标题： No-arbitrage and hedging with liquid American options

摘要： 由于大多数针对个股的交易期权为美式期权，因此将半静态交易中得到的结果推广到允许静态交易美式期权的情况是有意义的。 然而，由于持有与卖空这类期权存在不对称性质，这个问题迄今为止一直难以解决。 在这里，我们提供了一个统一框架，并将arXiv:1502.06681（即将发表于《应用概率年鉴》）中的资产定价基本定理（FTAP）和套期保值对偶性推广到投资者也可以卖空美式期权的情形。 按照arXiv:1502.06681的方法，我们假设持有的美式期权是可以分割的。 至于卖空的美式期权，我们证明了分割性对于套利特性和套期保值价格没有影响。 然后，利用arXiv:1604.05517中提出的扩展概率空间的方法，我们将卖空的美式期权转换为欧式期权，并在扩展后的空间中建立了FTAP以及带和不带模型不确定性的次套期保值和超套期保值对偶性。 显示英文摘要

摘要： Since most of the traded options on individual stocks is of American type it is of interest to generalize the results obtained in semi-static trading to the case when one is allowed to statically trade American options. However, this problem has proved to be elusive so far because of the asymmetric nature of the positions of holding versus shorting such options. Here we provide a unified framework and generalize the fundamental theorem of asset pricing (FTAP) and hedging dualities in arXiv:1502.06681 (to appear in Annals of Applied Probability) to the case where the investor can also short American options. Following arXiv:1502.06681, we assume that the longed American options are divisible. As for the shorted American options, we show that the divisibility plays no role regarding arbitrage property and hedging prices. Then using the method of enlarging probability spaces proposed in arXiv:1604.05517, we convert the shorted American options to European options, and establish the FTAP and sub- and super-hedging dualities in the enlarged space both with and without model uncertainty.