A reader asked: “Can you elaborate on high frequency trading order executions and possibly on corresponding techniques?”
The stream of formal research in the public domain on high-frequency trading is relatively thin. A title/abstract search in SSRN for the phrase “high frequency trading” generates just seven papers (with two of the seven offering abstracts only). The most heavily downloaded of the seven is:
“Dynamic Programming and Optimal Lookahead Strategies in High Frequency Trading with Transaction Costs”: “An optimal stochastic discrete time control problem with non smooth penalty function is considered. This problem naturally arises in high-frequency trading on financial markets. The principle of dynamic programming is formulated for this problem. Existence and uniqueness of the optimal strategy is proved. An algorithm for building a suboptimal strategy is presented and approximating properties of this strategy are studied. In addition, a simplified strategy is described which is a solution of an isotonic regression problem. A class of problems is defined on which this strategy can replace the basic suboptimal strategy. The results are illustrated by examples.”
Relaxing the search to “high frequency” yields many more papers, but relating them to your question is difficult.
A broader web search of the phrase “high frequency trading” that is limited to .pdf document types and .edu domain types yields more results, such as:
“High-frequency Trading in a Limit Order Book”: “In this paper, we study the optimal submission strategies of bid and ask orders in such a limit order book.”
“Statistical Arbitrage in High Frequency Trading Based on Limit Order Book Dynamics”: “We first built a “simulated” exchange order matching engine which allows us to reconstruct the order book. Therefore, in theory, we’ve built an exchange system which allows us to not only back-test our trading strategies but also evaluate the price impacts of trading. And we then implemented, calibrated and tested the Rama Cont model on both simulated data and real data. We also implemented, calibrated and tested an extended model. Based on these models and based on the order book dynamics, we explored a few high frequency trading strategies.”
“Financial Modeling: A System to Test High-Frequency Trading Strategies”: “This project has two objectives: One to provide a platform that allows simulating trades at ultra-high frequencies and allows investors to back-test trading strategies using historical data. The other, is to prove the hypothesis that when trading at very high frequencies and at very small time intervals, the correlation between assets breaks down in a non-linear way, and to demonstrate a strategy that exploits this statistical property to make money.”
You may be able to devise other searches that focus on specific aspects of high-frequency trading.
The above papers appear to be relatively complex and mathematics-intensive.
