Price Manipulation and Quasi-Arbitrage

In an environment where trading volume affects security prices and where prices are uncertain when trades are submitted, quasi-arbitrage is the availability of a series of trades that generate infinite expected profits with an infinite Sharpe ratio. We show that when the price impact of trades is permanent and time-independent, only linear price-impact functions rule out quasi-arbitrage and thus support viable market prices. When trades have also a temporary price impact, only the permanent price impact must be linear while the temporary one can be of a more general form. We also extend the analysis to a time-dependent framework.