Before revision:  We take the exchange to be an order-driven market and propose a continuous-time setup for the best bid price and the market spread, both modelled by Levy processes. In the situation where the trades take place only in the exchange, we find that the optimal execution strategy depends significantly on the dynamics of the limit order book .
After revision:  We take the exchange to be an order-driven market and propose a continuous-time setup for the best bid price and the market spread, both modelled by L\'evy processes. Effects on the best bid price arising from the arrival of limit buy orders at more favourable prices, the incoming market sell orders potentially walking the book, and deriving from the cancellations of limit sell orders at the best ask price are incorporated in the proposed price dynamics. A permanent impact that occurs when 'lit' pool trades cannot be avoided is built in, and an instantaneous impact that models the slippage, to which all 'lit' exchange trades are subject, is also considered .