Dynamic Modeling of Limit Order Book and Market Maker Strategy Optimization Based on Markov Queue Theory

Fei Xie, Yang Liu, Changlong Hu and Shenbao Liang ()
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Fei Xie: School of Finance, Shanghai University of Finance and Economics, Shanghai 200090, China
Yang Liu: School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200090, China
Changlong Hu: School of Statistics and Data Science, Shanghai University of Finance and Economics, Shanghai 200090, China
Shenbao Liang: School of Law, Shanghai University of Finance and Economics, Shanghai 200433, China

Mathematics, 2025, vol. 13, issue 5, 1-28

Abstract: In recent years, high-frequency trading has become increasingly popular in financial markets, making the dynamic modeling of the limit book and the optimization of market maker strategies become key topics. However, existing studies often lacked detailed descriptions of order books and failed to fully characterize the optimal decisions of market makers in complex market environments, especially in China’s A-share market. Based on Markov queue theory, this paper proposes the dynamic model of the limit order and the optimal strategy of the market maker. The model uses a state transition probability matrix to refine the market diffusion state, order generation, and trading process and incorporates indicators such as optimal quote deviation and restricted order trading probability. Then, the optimal control model is constructed and the reference strategy is derived using the Hamilton–Jacobi–Bellman (HJB) equation. Then, the key parameters are estimated using the high-frequency data of Ping An Bank for a single trading day. In the empirical aspect, the six-month high-frequency trading data of 114 representative stocks in different market states such as the bull market and bear market in China’s A-share market were selected for strategy verification. The results showed that the proposed strategy had robust returns and stable profits in the bull market and that frequent capture of market fluctuations in the bear market can earn relatively high returns while maintaining 50% of the order coverage rate and 66% of the stable order winning rate. Our study used Markov queuing theory to describe the state and price dynamics of the limit order book in detail and used optimization methods to construct and solve the optimal market maker strategy. The empirical aspect broadens the empirical scope of market maker strategies in the Chinese market and studies the stability and effectiveness of market makers in different market states.

Keywords: limit order book; Markov queuing theory; optimal market-making strategy; finite difference method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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