2013/10/07 by Pietro Fodra, Huyên Pham, Fodra, Pietro +1
Decision Sciences · Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Economics and business #FOS: Mathematics #Financial Markets and Investment Strategies #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications #Trading and Market Microstructure (q-fin.TR)
paper · pdf · doi:10.48550/arxiv.1310.1756
openalex publication_date 2013/10/07 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We study a an optimal high frequency trading problem within a market\nmicrostructure model designed to be a good compromise between accuracy and\ntractability. The stock price is driven by a Markov Renewal Process (MRP),\nwhile market orders arrive in the limit order book via a point process\ncorrelated with the stock price itself. In this framework, we can reproduce the\nadverse selection risk, appearing in two different forms: the usual one due to\nbig market orders impacting the stock price and penalizing the agent, and the\nweak one due to small market orders and reducing the probability of a\nprofitable execution. We solve the market making problem by stochastic control\ntechniques in this semi-Markov model. In the no risk-aversion case, we provide\nexplicit formula for the optimal controls and characterize the value function\nas a simple linear PDE. In the general case, we derive the optimal controls and\nthe value function in terms of the previous result, and illustrate how the risk\naversion influences the trader strategy and her expected gain. Finally, by\nusing a perturbation method, approximate optimal controls for small risk\naversions are explicitly computed in terms of two simple PDE's, reducing\ndrastically the computational cost and enlightening the financial\ninterpretation of the results.\n