Before revision:  We use such characterizations to study when a market maker can earn a positive net profit and investigate the effect of latency. Numerical experiments are conducted to illustrate our results .
After revision:  We use such characterizations to study when 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 .