  This paper studies optimal market making for large-tick assets in the
presence of latency. We consider a random walk model for the asset price, and
formulate the market maker's optimization 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 expected profit if there are sufficient uninformed market orders
hitting the market maker's limit orders compared with the rate of price jumps,
and the trading horizon is sufficiently long. In addition, our theoretical and
numerical results suggest that latency can be an additional source of risk and
latency impacts negatively the performance of market makers.
