2021/12/01 by Bastien Baldacci, Baldacci, Bastien, Philippe Bergault +1 · 1 citation
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Economics and business #FOS: Mathematics #Financial Markets and Investment Strategies #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Stochastic processes and financial applications #Trading and Market Microstructure (q-fin.TR)
paper · doi:10.48550/arxiv.2112.00375
openalex publication_date 2021/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
With the fragmentation of electronic markets, exchanges are now competing in order to attract trading activity on their platform. Consequently, they developed several regulatory tools to control liquidity provision / consumption on their liquidity pool. In this paper, we study the problem of an exchange using incentives in order to increase market liquidity. We model the limit order book as the solution of a stochastic partial differential equation (SPDE) as in [12]. The incentives proposed to the market participants are functions of the time and the distance of their limit order to the mid-price. We formulate the control problem of the exchange who wishes to modify the shape of the order book by increasing the volume at specific limits. Due to the particular nature of the SPDE control problem, we are able to characterize the solution with a classic Feynman-Kac representation theorem. Moreover, when studying the asymptotic behavior of the solution, a specific penalty function enables the exchange to obtain closed-form incentives at each limit of the order book. We study numerically the form of the incentives and their impact on the shape of the order book, and analyze the sensitivity of the incentives to the market parameters.