Under short-sales prohibitions, no free lunch with vanishing risk (NFLVRS) is known to be equivalent to the existence of an equivalent supermartingale measure for the price process (Pulido in Ann. Appl. Probab. 24:54–75, 2014). We give a necessary condition for the drift of a price process to satisfy NFLVRS. For two given price processes, we introduce the concept of fundamental supermartingale measure, and when a certain condition necessary for the construction of this fundamental supermartingale measure is not fulfilled, we provide the corresponding arbitrage portfolios. The motivation of our study lies in understanding the particular case of converging prices, i.e., two prices that coincide at a bounded random time.

中文翻译：

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卖空限制下的一些无套利规则，以及在资产价格趋同中的应用

在禁止卖空的情况下，没有任何具有消失风险的免费午餐（NFLVRS）等同于存在用于价格过程的等效超级市场措施（Pulido in Ann。Appl。Probab。24：54-75，2014）。我们为价格过程的漂移提供了满足NFLVRS的必要条件。对于两个给定的价格过程，我们引入了基本超级市场测度的概念，并且当不满足构建该基本超级市场测度的必要条件时，我们将提供相应的套利组合。我们研究的动机在于理解收敛价格的特殊情况，即，两个价格在有限的随机时间重合。