Optimization of stock trading with additional information by Limit Order Book

Nowadays stocks and futures are traded in electronic order-driven markets, in which orders to buy and sell are centralized in a Limit Order Book (LOB), and LOB provides more information about the stocks than their prices, such as the price dynamics and the prediction probability of the next move. In this paper, we investigate how and why Limit Order Book can improve the trading decision making. We propose a conditional binomial model for a stock price with conditional upward probability based on observations. We formulate the stock portfolio management as an optimization problem with observations, and optimal schemes are given for single-stock and multi-stock portfolios with observations. Compared with the strategies that do not consider the observations, we show that the final expected wealth achieves significant improvements. Finally, two real-data-based examples are conducted to demonstrate the efficiency of our schemes. Our work points to a new direction in improving the final wealth in portfolio management; and it illustrates the advantages of event-based optimization approach, which was successfully applied in discrete event dynamics systems.