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.