I'm recently reading several papers on modelling stock order behavior and its corresponding optimal strategies. Compared with classical quantitative trading strategies, serious research on order optimization has a short history as its major importance dazzles in high frequency trading (HFT), one of the youngest childs of finance. I'll wrap up the main ideas and methodologies below in a paper-wise manner. Further unregular updates on this post are expected. Specifically, the models below are trying to answer this question: how much time should I expect before my limit order gets executed?