Before revision:  The resulting demand curve constitutes the sole input to our model. The clearing price is then mechanically calculated using the market clearing condition. We model liquidity by considering the impact of a large trader on the market and on the clearing price. We assume a continuous model for the demand curve. We show that generically there exists an equivalent martingale measure for the clearing price , for all possible strategies of the large trader, if the driving noise is a Brownian sheet, while there may not be if the driving noise is multidimensional Brownian motion.
After revision:  The resulting demand curve constitutes the sole input to the model. We prove that generically there is no arbitrage in the model when the driving noise is a stochastic string. Under the equivalent martingale measure for the clearing price , for all possible strategies of the large trader, if the driving noise is a Brownian sheet, while there may not be if the driving noise is multidimensional Brownian motion.