Abstract
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 processes (Pulido, 2014).We give a necessary condition for the drift of a price process to satsify (NFLVRS). For two given price processes, we introduce the concept of fundamental supermartingale measure, and when a certain condition necessary to 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.
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