Before revision:  We also prove that higher latency leads to reduced profits for market makers, and conduct numerical experiments to illustrate the effect of latency and relative latency on the market maker's expected profit. Finally, our work highlights the importance of value of orders in optimal market making .
After revision:  We also prove that higher latency leads to reduced profits for market makers, and conduct numerical experiments to illustrate the effect of latency . Numerical experiments are conducted to illustrate our results .