Before revision:  We formulate the problem using Markov Decision Processes . We provide explicit characterizations of the order value and the structure of the value functions. We use such characterizations to study when a market maker can earn a positive net profit and investigate the effect of latency.
After revision:  We formulate the problem using Markov Decision Processes (MDP). We characterize the value of an order and show that it plays the role of one-period reward in the MDP model. Based on this characterization, we provide explicit criteria for assessing the profitability of market making when there is latency. Under our model, we show that a market maker can earn a positive net profit and investigate the effect of latency.